Answer:
y = [tex]\frac{fa - 24}{15}[/tex]
Step-by-step explanation:
[tex]\frac{15y + 24}{a}[/tex] = f
multiply both sides by a
(15y + 24) = fa
the parenthesis can be removed
15y + 24 = fa
subtract 24 from both sides
15y = fa - 24
divide both sides by 15
y = [tex]\frac{fa - 24}{15}[/tex]
PLEASE HELP!!!!!!!!! LOOK AT PIC, THANKS!!!!!!
Answer:
F (x) = 1,6
Step-by-step explanation:
my answer is due to the reason that it is one of the three options and it should only in a way make sense that it is the right answer
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. what is the solution set of this problem? (negative infinity, negative 21) (negative infinity, negative 21 right-bracket left-bracket negative 21, positive infinity) (21, positive infinity)
The solution set of Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26 is x ≤ 21
What is Inequality?Inequalities are expressions that have <, >, ≤ or ≥. Therefore,
let the number = x
Five times the sum of a number and 27 is as follows:
5(x + 27)
Six times the sum of that number and 26 is as follows:
6(x + 26)
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26 is as follows:
5(x + 27) ≥ 6(x + 26)
Therefore,
5(x + 27) ≥ 6(x + 26)
5x + 135 ≥ 6x + 156
-x ≥ 21
x ≤ 21
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Answer:
ITS B
Step-by-step explanation:
took the test
h + r when b = 3, d = 12, h = 2 and r = 7.
Answer:
The answer to your question is 3
Step-by-step explanation:
2 + 7 = 9
9÷3 = 3
25 POINTS AND BRAINLIEST
17. A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 9 hours. Paulo can paint the same room in 8 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth.
Answer:
4.24 hours
Step-by-step explanation:
Irina can paint 1/9 of a room in 1 hour since she can paint a room in 9 hours. 1/9x, where x is the number of hours she works and 1/9 of a room per hour is her speed, would be her part of the calculation.
Paulo can paint 1/8 of a room in 1 hour since he can paint an entire room in 8 hours. 1/8x, where x is the number of hours he works and 1/8 of a room per hour is his speed, would be his part of the equation.
1/9x + 1/8x = 1 (Irina's portion of the room plus Paulo's portion of the room equals one complete room) would be the equation.
Look for a denominator that has the same value as the numerator. Both 9 and 8 split evenly into 72 as the initial number. We multiply the top of 1/9 by 8 to convert the fraction and get 8/72x because 9*8 = 72. We multiply the top of 1/8 by 9 to convert the fraction and get 9/72x because 8*9 = 72. We have 8/72x+9/72x=1 currently.
17/72x=1
÷ both sides by 17/72:
17/72x ÷ 17/72 = 1÷17/72
∴ x=1/1 * 72/17
∴ x=72/17= 4.24
Which fraction is equal to 0.25.?
Answer: 1/4
Step-by-step explanation:
Hope this helps
The 0.25 is equivalent to 1/4, where the numerator is 1 and the denominator is 4.
The fraction that is equal to 0.25 is 1/4. To understand this, examine the decimal representation of 0.25. The decimal point separates the whole number part from the fractional part. In 0.25, the digit 2 is in the tenths place, and the digit 5 is in the hundredths place. As a fraction, the number 2 in the tenths place can be written as 2/10, and the number 5 in the hundredths place written as 5/100. Simplifying these fractions, find that 2/10 reduces to 1/5 and 5/100 reduces to 1/20.
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No links and just the answer and explanation
Answer:
x = 1, x = 6
Step-by-step explanation:
Given equation:
[tex]\dfrac{x+2}{x-4}=\dfrac{2x}{x-3}[/tex]
Cross multiply:
[tex]\implies (x+2)(x-3)=2x(x-4)[/tex]
Expand brackets:
[tex]\implies x^2-3x+2x-6=2x^2-8x[/tex]
[tex]\implies x^2-x-6=2x^2-8x[/tex]
Collect and combine like terms:
[tex]\implies 2x^2-x^2-8x+x+6=0[/tex]
[tex]\implies x^2-7x+6=0[/tex]
Factor:
[tex]\implies (x-6)(x-1)=0[/tex]
Therefore,
[tex](x-6)=0\implies x=6[/tex]
[tex](x-1)=0 \implies x=1[/tex]
Now, determine whether the relationship between the two triangles you found in the first task is true for any two triangles. For any line, if you draw two right triangles using the line as the hypotenuse, can the triangles be congruent? Why or why not? Do they have to be congruent? Why or why not?
Answer:
The two triangles are not congruent.
Step-by-step explanation:
If two right triangles are drawn with a line as hypotenuse, the two triangles are not congruent. Because as per RHS congruency ie Right Angle - Hypotenuse - Side : right angle, hypotenuse & also one other side equality is needed for congruence. Given case doesn't satisfy the last 'other side equality' condition.
Answer:
h
Step-by-step explanation:
What is the rate of change of function B
Answer:
I THINK ITS 20 BUT I AM NOT SURE
Jacqueline drove 72 km on 6 L of gasoline.
Which of the following equations can be used to find how far she can travel on a full tank of 50 L?
A. 6/72=x/50
B. 72/6=50/x
C. x/72=6/50
D. 6/72=50/x
Answer:
6/72=50/x
Step-by-step explanation:
I just took the test and got it correct
What is the equivalent expression for the following: 10^6 ÷ 10^4
a:
10^24
b:
1
c:
10^2
d:
10^10
9514 1404 393
Answer:
c. 10^2
Step-by-step explanation:
It can be helpful to remember that an exponent signifies repeated multiplication. Here, the denominator factors cancel an equal number of numerator factors
[tex]\dfrac{10^6}{10^4}=\dfrac{10\cdot10\cdot10\cdot10\cdot10\cdot10}{10\cdot10\cdot10\cdot10}=10\cdot10=\boxed{10^2}[/tex]
For the first 80 miles of her road trip, Lina travels 10 miles/hour slower than she did for the remaining 50 miles of her trip. If srepresents Lina's
speed during the first part of her trip, which expressions represent the total time of her trip in hours?
( The picture are the answer choices!!!)
Answer:
Option (5)
Step-by-step explanation:
Lina's speed during the first part of the trip = s miles per hour
If she travels initial 80 miles on this trip with this speed, time taken to cover the distance [tex]t_1=\frac{\text{Distance}}{\text{Speed}}=\frac{80}{s}[/tex] hours
Now speed at which she traveled remaining 50 miles = (s + 10) miles per hour
So the time spent to cover this distance [tex]t_2=\frac{50}{s+10}[/tex] hours
Total time for the complete trip = [tex]t_1+t_2[/tex] = [tex]\frac{80}{s}+\frac{50}{s+10}[/tex]
= [tex]\frac{80(s+10)+50s}{s(s+10)}[/tex]
= [tex]\frac{80s+800+50s}{s(s+10)}[/tex]
= [tex]\frac{130s+800}{s(s+10)}[/tex]
Therefore, Option (5) will be the answer.
Option C is correct. The expressions that represent the total time of her trip in hours is [tex]t_1 + t_2 = \frac{80}{s} +\frac{50}{s+10} \\[/tex]
Let the speed travelled during the first part of the trip be "s"
The formula for calculating the distance is expressed as:
[tex]distance=speed\times time[/tex]
For the first part of the journey:
distance = 80miles
time = t₁
Speed = s
Substitute the given parameters into the formula:
[tex]80 = st_1\\t_1=\frac{80}{s}[/tex]........................................... 1
For the second part of the trip;
Distance travelled = 5 miles
speed = s + 10 (10miles/hour faster than the first part of the trip)
time = t₂
Get the time t₂
[tex]50=(s+10)t_2\\t_2=\frac{50}{s+10}[/tex]
Adding both times taken to get the total time of her trip in hours.
[tex]t_1 + t_2 = \frac{80}{s} +\frac{50}{s+10} \\[/tex]
Hence the expression that represent the total time of her trip in hours is [tex]t_1 + t_2 = \frac{80}{s} +\frac{50}{s+10} \\[/tex]
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This triangular arrangement, known as Pascal's triangle, generates numbers based on a pattern. Fill in the missing numbers. Pascal's triangle Row 1: 1, Row 2: 1, 1. Row 3: 1, 2, 1. Row 4: 1, 3, 3, 1. Row 5: 1, 4, 6, 4, 1. Row 6: 1, 5, 10, 10, 5, 1. Row 6: 1, 6, 15, 20, 15, 6, 1. Row 7: 1, blank, blank, blank, blank, blank, blank, 1. A. 2, 3, 4, 5, 6, 7 b. 8, 21, 35, 21, 20, 8 c. 7, 20, 35, 35, 20, 7 d. 7, 21, 35, 35, 21, 7
Answer: D.) 7, 21, 35, 35, 21, 7
Step-by-step explanation:
For pascal triangle :
Row 1: 1,
Row 2: 1, 1.
Row 3: 1, 2, 1.
Row 4: 1, 3, 3, 1.
Row 5: 1, 4, 6, 4, 1.
Row 6: 1, 5, 10, 10, 5, 1.
Row 6: 1, 6, 15, 20, 15, 6, 1.
Row 7: 1, blank, blank, blank, blank, blank, blank, 1
To obtain values for any row :
Digit 1 is plaved at both extremes ; and each two successive digit in the previous row is added to obtain the numbers in that row.
For row 7:
After placing 1 at both extremes ;
Each two successive digits in row 6 are summed up;
Row 6: 1, 6, 15, 20, 15, 6, 1.
(1 + 6) = 7;
(6 + 15) = 21
(15 + 20) = 35
(20 + 15) = 35
(15 + 6) = 21
(6 + 1) = 7.
Hence,
Row 7 = 1, 7, 21, 35, 35, 21, 7, 1
Which is the graph of the linear inequality 2x – 3y < 12?
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
Mark this and return
Answer:
see graph
Step-by-step explanation:
the number which is 3 less than the product of x and y
Answer:
xy - 3
Step-by-step explanation:
Product of x and y = xy
Required number = xy - 3
Answer:cycle-3
Step-by-step explanation:
Please can somebody solve this this is due today
The diameter of a cylinder is 7 yd. The height is 4 yd Find the volume of the cylinder.
Cylinder volume = base area x height
= pi x r² x h
d = 7 yd => r = 7:2 = 3,5 yd
and h = 4 yd
to be calculed
V = 3,14 x 3,5² x 4
out of every five girls are wearing ribbons if there are 60 girls in the school how many of them were wearing ribbons
Answer:
12
Step-by-step explanation:
if you dived 60 by 5 you get 12, I dived because if you do groups of 5 until you get to 60 you can make 12 groups
Help me out on this one also please
Answer:
B the range of f (-00,-4)
Answer:
A and D
Step-by-step explanation:
A is correct as x must be any real number to yield a proper f(x) value.
B is incorrect, as a value of x=0 would mean f(x) = 0 which is outside the listed range.
C is incorrect as the equation is a quadratic (highest exponent is ^2) which forms a parabola shape on a graph and therefore does not infinitely decrease.
D is correct. To find a maximum or turning point, we can take the derivative of the function and set it to 0, as the slope at any turning point will always be 0:
f'(x) = -8x
0 = -8x
x = 0
So, the maximum occurs where x=0
f(x) = -4x^2
f(x) = -4(0)^2
f(x) = 0
This means the y-value is also 0, meaning that (0,0) is our maximum.
E is incorrect. Since the maximum is only just on the x-axis (0,0) it only touches the x-axis once so it only has one x-intercept.
Hope this helped!
The boxplot displays a summary of 20 test scores.
A boxplot. The number line goes from 22 to 82. The whiskers range from 23 to 81, and the box ranges from 60 to 73. A line divides the box at 61.8.
ANSWERS
Complete the statements based on the boxplot.
This distribution of test scores is skewed left. The test score of 23 is an outlier. The median test score is 61.5. The range of all of the test scores is 58, while the range of the middle 50 percent of the test scores is 13.
Answer:
Skewed left
is
61.5
58
13
Step-by-step explanation:
The missing statements are skewed left, Outlier, score and scores; range; scores.
1. This distribution of test scores is skewed left.
The distribution is skewed left because the tail of the boxplot extends to the left, indicating that there are more lower scores in the dataset.
2. The test score of 23 is an outlier.
The value 23 is an outlier since it lies outside the whiskers of the boxplot. An outlier is a data point that is significantly different from the rest of the data.
3. The median test score is 61.5.
The median is the value that separates the data into two equal halves. Since the line divides the box at 61.8, the median is 61.5.
4. The range of all the test scores is
= 81 - 23
= 58.
The range of the middle 50 percent is the difference between the upper quartile and the lower quartile, which is given as (73 - 60) = 13.
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A laboratory technician needs to make a 40-liter batch of a 40% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 20% to get the desired
concentration?
The laboratory technician can combine L of the pure acid solution with L
of the 20% acid solution to get the desired concentration
Answer:
The technician can combine 10 liters of pure acid with 30 liters of 20% acid to get the desired concentration
Step-by-step explanation:
For pure acid, the concentration will be 100%
Let the liters of pure be a and the liters of 20% be b
Since we want 40 liters of total;
a + b = 40 ••••••••(i)
Also,
100% of a + 20% of b = 40% of 40
a + 0.2b = 16 •••••(ii)
From ii , a = 16-0.2b
Put this into i
16-0.2b + b = 40
0.8b = 40-16
0.8b = 24
b = 24/0.8
b = 30
Since a + b = 40
a = 40 - b
a = 40-30
a = 10
PLS HELP WITH THIS TRANSLATION, IDK HOW TO DO IT
(-3,6) == (-1,1)
-3 + 2 = -1 ,
6 -5 = 1
(-3,3) == (-1,-2)
-3 + 2 = -1
3 - 5 = -2
(-5,3) == (-3,-2)
-5 + 2 = -3
3 - 5 = -2
The magnitude, m, of an earthquake is defined to be m = log startfraction i over s endfraction, where i is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and s is the intensity of a "standard" earthquake, which is barely detectable. what is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? use a calculator. round your answer to the nearest tenth. 2 3 4.5 6.9
The magnitude, M, of an earthquake is 1.544 units when the magnitude of an earthquake is 1,000 times more intense than a standard earthquake
It is given that the magnitude of m, of an earthquake, is defined as:
[tex]\rm M=log\frac{I}{S}[/tex]
Where 'I' is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and 'S' is the intensity of a "standard" earthquake.
It is required to find the magnitude of the earthquake that is 1,000 times more intense than a standard earthquake.
What is Logarithm?It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b=c\\\rm log_ac=b[/tex]
We have:
[tex]\rm M=log\frac{I}{S}[/tex]
and [tex]\rm I=35S[/tex] putting this value in the above equation, we get:
[tex]\rm M=log\frac{35S}{S}[/tex]
[tex]\rm M=log35[/tex]
[tex]\rm M=1.544[/tex] (From log table)
Thus, The magnitude, M, of an earthquake is 1.544 units.
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Answer:
M=3
Step-by-step explanation:
A circle has a diameter of 16 inches what is the area of the circle in terms of π(pi)
Answer:
64π Inches squared
Step-by-step explanation:
A=πr^2
Half of 16 is 8
r=8
A=π8^2
A=64π
The pavement at the new shopping mall is being laid. Which transformation is applied from brick A to brick B?
rotation
translation
dilation
reflection
Answer:
I WOULD SAY ITS rotaiton UWU
Rotation is the transformation applied from brick A to brick B.
We need to find which transformation is applied from brick A to brick B.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, line, or geometric figure.
Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point.
Brick A rotated 90° to brick B.
Therefore, rotation is the transformation applied from brick A to brick B.
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Can someone help me on this question? I’ve been struggling on this for a while now. I’ll give brainliest if you answer soon!!!
A. What convinces you that the February 29 image is a reflection of the February 28 image about the given line of reflection?
B. What convinces you that the March 1 image is a reflection of the February 29 image about the given line of reflection?
C. What convinces you that the two reflections together complete a rotation between the February 28 and March 1 images?
Answer:
A. Line of reflection is a perpendicular bisector
B. 90 degree angles, equal lines
C. Pre-image an image are on the same circle.
Step-by-step explanation:
I hope this helped you in any way possible. :)
Tom is 8 years younger than John. Let j represent John's age in years. Write an algebraic expression to represent Tom's age in years.
Answer:
(j-8)years is the answer to the question
Imagine that several of your blog’s readers say they want to eat more locally grown food but are not sure where to buy it. What would the best response be?
Local Farmers' Markets, CSA, Local Grocery Stores, Online Resources are the best responses to the readers.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The best response would be to provide your readers with a list of resources for finding locally grown food. Here are some suggestions:
Local Farmers' Markets: Farmers' markets are a great place to find locally grown food.
Community Supported Agriculture: CSA programs allow you to purchase a share of a local farm's produce for the season.
Local Grocery Stores: Many grocery stores now carry locally grown produce and other food products
Online Resources : There are many websites that can help you find locally grown food.
Local Farms: Some local farms have their own stores or farm stands where they sell their products directly to consumers.
Hence, by providing your readers with these resources, they will have a better understanding of where to find locally grown food and how to support their local food system.
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13. Which line has a positive slope and a positive y-intercept?
Line B has a positive slope and a positive y-intercept because crosses the y-axis above the origin.
As per the shown graph,
In line A, we move from left to right along the line, and the y-values decrease. This means line A has a negative slope.
In line B, we move from left to right along the line, and the y-values increase. This means line B has a positive slope.
Similarly, line C has a positive slope.
Here, lines A and B cross the y-axis above the origin (positive y-intercept)
Thus, line B has a positive slope and a positive y-intercept.
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find the unit rate if 20 snickers bar cost $10
Answer: 50
Step-by-step explanation:
20 divided by 10 is 2, and a half a dollar is 50 cents.
Ultraviolet light from a distant star is traveling at 3. 0 × 108 m/s. How long will it take for the light to reach Earth if it must travel 4. 0 × 1013 km? 2. 7 × 10–2 hours 2. 2 × 103 hours 3. 7 × 104 hours 1. 3 × 105 hours.
The time taken for the light to reach earth will be 3.6 ×10⁴ hours. The quantity of time that an activity or a condition continues to exist. is known as the time period.
What is the time period?The amount of time that an action or a state continues to exist. is the time period. Depending on the nature of the activity or situation under consideration, it might be measured in seconds or millions of years.
The given data in the problem is;
v is the speed of ultraviolet light= 3 ×10⁸ m/sec
d is the distance covered by the light= 4×10¹³ Km=4× 10¹⁶m
The time taken by the light to reach the surface of the earth will be;
[tex]\rm d = v\times t \\\\ \rm t= \frac{d}{v} \\\\ \rm t= \frac{4\times 10^{16}}{3\times 10^8} \\\\ \rm t= 1.33 \times 10^{8} \ sec[/tex]
In one hour there are 3600 seconds so the time period in the hours is found as;
[tex]\rm t= 1.33 \times 10^8 \times \frac{1}{3600} \\\\ \rm t=3.6 \times 10^4\ hours[/tex]
Hence the time taken for the light to reach earth will be 3.6 ×10⁴ hours.
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Answer:
C. 3. 7 × 104 hours
Step-by-step explanation:
write the equation for the function that has the shape of f(x)=x^3 but is moved three units to the left, seven units upward, and then reflected in the x-axis?
Answer:
The first transformation occurs when we add a constant d to the parent function \displaystyle f\left(x\right)={b}^{x}f(x)=b
x
, giving us a vertical shift d units in the same direction as the sign. For example, if we begin by graphing a parent function, \displaystyle f\left(x\right)={2}^{x}f(x)=2
x
, we can then graph two vertical shifts alongside it, using \displaystyle d=3d=3: the upward shift, \displaystyle g\left(x\right)={2}^{x}+3g(x)=2
x
+3 and the downward shift, \displaystyle h\left(x\right)={2}^{x}-3h(x)=2
x
−3. Both vertical shifts are shown in Figure 5.
Graph of three functions, g(x) = 2^x+3 in blue with an asymptote at y=3, f(x) = 2^x in orange with an asymptote at y=0, and h(x)=2^x-3 with an asymptote at y=-3. Note that each functions’ transformations are described in the text.
Figure 5
Observe the results of shifting \displaystyle f\left(x\right)={2}^{x}f(x)=2
x
vertically:
The domain, \displaystyle \left(-\infty ,\infty \right)(−∞,∞) remains unchanged.
When the function is shifted up 3 units to \displaystyle g\left(x\right)={2}^{x}+3g(x)=2
x
+3:
The y-intercept shifts up 3 units to \displaystyle \left(0,4\right)(0,4).
The asymptote shifts up 3 units to \displaystyle y=3y=3.
The range becomes \displaystyle \left(3,\infty \right)(3,∞).
When the function is shifted down 3 units to \displaystyle h\left(x\right)={2}^{x}-3h(x)=2
x
−3:
The y-intercept shifts down 3 units to \displaystyle \left(0,-2\right)(0,−2).
The asymptote also shifts down 3 units to \displaystyle y=-3y=−3.
The range becomes \displaystyle \left(-3,\infty \right)(−3,∞).
Graphing a Horizontal Shift
The next transformation occurs when we add a constant c to the input of the parent function \displaystyle f\left(x\right)={b}^{x}f(x)=b
x
, giving us a horizontal shift c units in the opposite direction of the sign. For example, if we begin by graphing the parent function \displaystyle f\left(x\right)={2}^{x}f(x)=2
x
, we can then graph two horizontal shifts alongside it, using \displaystyle c=3c=3: the shift left, \displaystyle g\left(x\right)={2}^{x+3}g(x)=2
x+3
, and the shift right, \displaystyle h\left(x\right)={2}^{x - 3}h(x)=2
x−3
. Both horizontal shifts are shown in Figure 6.
Graph of three functions, g(x) = 2^(x+3) in blue, f(x) = 2^x in orange, and h(x)=2^(x-3). Each functions’ asymptotes are at y=0Note that each functions’ transformations are described in the text.
Figure 6
Observe the results of shifting \displaystyle f\left(x\right)={2}^{x}f(x)=2
x
horizontally:
The domain, \displaystyle \left(-\infty ,\infty \right)(−∞,∞), remains unchanged.
The asymptote, \displaystyle y=0y=0, remains unchanged.
The y-intercept shifts such that:
When the function is shifted left 3 units to \displaystyle g\left(x\right)={2}^{x+3}g(x)=2
x+3
, the y-intercept becomes \displaystyle \left(0,8\right)(0,8). This is because \displaystyle {2}^{x+3}=\left(8\right){2}^{x}2
x+3
=(8)2
x
, so the initial value of the function is 8.
When the function is shifted right 3 units to \displaystyle h\left(x\right)={2}^{x - 3}h(x)=2
x−3
, the y-intercept becomes \displaystyle \left(0,\frac{1}{8}\right)(0,
8
1
). Again, see that \displaystyle {2}^{x - 3}=\left(\frac{1}{8}\right){2}^{x}2
x−3
=(
8
1
)2
x
, so the initial value of the function is \displaystyle \frac{1}{8}
8
1
.
A GENERAL NOTE: SHIFTS OF THE PARENT FUNCTION \DISPLAYSTYLE F\LEFT(X\RIGHT)={B}^{X}F(X)=B
X
For any constants c and d, the function \displaystyle f\left(x\right)={b}^{x+c}+df(x)=b
x+c
+d shifts the parent function \displaystyle f\left(x\right)={b}^{x}f(x)=b
x
vertically d units, in the same direction of the sign of d.
horizontally c units, in the opposite direction of the sign of c.
The y-intercept becomes \displaystyle \left(0,{b}^{c}+d\right)(0,b
c
+d).
The horizontal asymptote becomes y = d.
The range becomes \displaystyle \left(d,\infty \right)(d,∞).
The domain, \displaystyle \left(-\infty ,\infty \right)(−∞,∞), remains unchanged.
HOW TO: GIVEN AN EXPONENTIAL FUNCTION WITH THE FORM \DISPLAYSTYLE F\LEFT(X\RIGHT)={B}^{X+C}+DF(X)=B
X+C
+D, GRAPH THE TRANSLATION.
Draw the horizontal asymptote y = d.
Identify the shift as \displaystyle \left(-c,d\right)(−c,d). Shift the graph of \displaystyle f\left(x\right)={b}^{x}f(x)=b
x
left c units if c is positive, and right \displaystyle cc units if c is negative.
Shift the graph of \displaystyle f\left(x\right)={b}^{x}f(x)=b
x
up d units if d is positive, and down d units if d is negative.
State the domain, \displaystyle \left(-\infty ,\infty \right)(−∞,∞), the range, \displaystyle \left(d,\infty \right)(d,∞), and the horizontal asymptote \displaystyle y=dy=d.
Step-by-step explanation: