Part 3: The function f(x) = 2* is reflected vertically, translated 5 units
up and 3 units left to find g(x). (10 points per answer)
1. Write out the function g(x).
2. What is the domain of g(x)?
3. What is the range of g(x)?
Answers
Answer:
First, let's define the transformations in a general way.
Vertical translation:
A vertical translation of N units is defined as:
g(x) = f(x) + N
if N is positive, the translation is up
if N is negative, the translation is down.
Horizontal translation:
A horizontal translation of N units can be written as:
g(x) = f(x - N)
if N is positive, the translation is to the right
if N is negative, the translation is to the left.
Reflected vertically (or a reflection over the x-axis)
This type of reflection changes the sign of the y component.
We can write those as:
g(x) = -f(x)
Then:
We start with the function:
f(x) = 2^x
First we reflect it vertically.
g(x) = -2^x
now we do a vertical translation of 5 units up, then:
g(x) = -2^x + 5
Now we do a translation of 3 units to the left, then we get:
g(x) = - 2^(x + 3) + 5
Then we already did the first step.
Now we want to find the domain for this function, the domain will be the set of the possible values of x that we can input in the function g(x).
Notice that in this function the denominator is never zero, so there are no values of x that generate problems here, so the domain will be the set of all real numbers, that can be written as:
(-∞, ∞)
3) Now we want to find the range, this is the set of the possible values of g(x).
The Largest value of g(x) will be when the exponential part tends to zero, this is for really small values of x, such that when x goes to minus infinity, -2^(x + 3) goes to zero.
Then:
g(-∞) ≈ 5
The maximum of the range is 5.
And we do not have a minimum, because as x increases the function will decrease infinitely.
Then the range will be:
(-∞, 5)
(A graph of the function can be seen below)
Related Questions
Plz, Help me with this question.
Answers
6(3) - 2(4) = 18 - 8= 10
Answer:
F. 10
Step-by-step explanation:
6d - 2c
6 * 3 - 2 * 4
18 - 8
10
8. A school raffle sold 480 tickets. Students were charged $1/ticket and teachers $5/ticket. The total receipts were $560. How many of each ticket were sold? 9. An airplane travels 5432 km. On the outward trip it took 7 hours with the wind. On the return trip, it took 8 hours against the wind. What was the speed of the plane and the speed of the wind? (Remember: distance = speed x time)
Answers
Answer:
8. Number of student tickets = 460
Number of teacher tickets = 100
9. Speed of plane = 727.5 km/hr
Speed of wind = 48.5 km/hr
Step-by-step explanation:
8.
Let number of students' tickets = [tex]x[/tex]
Let number of teachers' tickets = [tex]y[/tex]
Total number of tickets = 480
[tex]x+y=480[/tex] ...... (1)
Price for one student's ticket = $1
Price for one teacher's ticket = $5
Total money collected by the tickets = $560
[tex]x +5y = 560[/tex] ...... (2)
Subtracting (1) from (2):
[tex]4y = 80\\\Rightarrow y = 20[/tex]
By equation (1):
[tex]x = 460[/tex]
Number of student tickets = 460
Number of teacher tickets = 100
9.
Let the speed of airplane in still air = [tex]u[/tex] km/hr
Let the speed of air = [tex]v[/tex] km/hr
Total distance = 5432 km
Time taken with the wind = 7 hours.
Speed with the wind = [tex]u+v[/tex] km/h
Time taken against the wind = 8 hours.
Speed with the wind = [tex]u-v[/tex] km/h
Using the formula:
Distance = Speed [tex]\times[/tex] Time
[tex]5432 = (u+v)\times 7\\\Rightarrow u +v = 776 .... (1)[/tex]
[tex]5432 = (u-v)\times 8\\\Rightarrow u - v = 679 .... (2)[/tex]
Adding (1) and (2):
[tex]2u = 1455\\\Rightarrow u = 727.5\ km/hr[/tex]
By equation (1):
[tex]v = 48.5\ km/hr[/tex]
Speed of plane = 727.5 km/hr
Speed of wind = 48.5 km/hr
Brenda and Melissa each have a band. Brenda's band plays songs in sets of 4 and Melissa's band plays songs in sets of 6. After performing together, both bands realize that they have played the same number of songs. What is the smallest number of songs each band could have performed?
Answers
Answer:
12 songs
Step-by-step explanation:
Brenda's band plays songs in sets of 4
Melissa's band plays songs in sets of 6.
After performing together, both bands realize that they have played the same number of songs.
What is the smallest number of songs each band could have performed?
The smallest number of songs each band could have performed can be calculated by finding the lowest common multiple of 4 and 6
4 = 8, 12, 16, 20, 24, 28, 32, 36, 40
6 = 12, 18, 24, 30, 36, 42
The lowest common multiple of 4 and 6 is 12
The smallest number of songs each band could have performed is 12 dongs
please help me with this
Answers
Answer:
B
Step-by-step explanation:
Jim is saving money to buy a game. So far he saved $36, which is three-fourths of the total cost of the game. How much does the game cost?
Answers
Answer:
$48
Step-by-step explanation:
Because he has 3/4 you would divide 36 by 3 whick is 12 then multiply by 4 to get the total of $48
Answer:
$48 :)
Step-by-step explanation:
Show work and I will give you brainliest
Answers
Answer: There is not enough info and I can't see because the picture is not clear enough. Sorry. :(
Merry (early) Christmas tho! :)
Find the slope of the line that passes through (10, 10) and (3, 1).
Answers
Answer:
-7/-9 pretty sure
Step-by-step explanation:
x2-x1
y2-y1
3-10= -7
1-10= -9
A real horse is 1.8 m high. A statue of the horse is 3 m high. What is the ratio of the height of the horse to the height of the statue
Answers
1.8/1.8 : 3/1.8 = 1:1.67 and there you go.
Please help I will give brainliest!!!
Answers
Answer:
I think it is C.
Step-by-step explanation:
Write the number in scientific notation
307,000,000
Answers
Answer:
3.07×10^8
Step-by-step explanation:
:)
hope this helps
Answer: 307,000,000 in scientific notation is 3.07 × 10^8.
PLEASE HELP ASAP!!!
3 + 2x² + 3x + 2x² + 5 = ?
Answers
Answer: 4x² + 3x + 8
Work: I combined Like Terms, put them in the right form, from the x² to the number.
I hope this helps and Happy Holidays! :)
Answer:
25
Step-by-step explanation:
3+2=5×2 ×2 +5=25
add the 10 to the other 10 and then add 5
A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet. What is the width of the sidewalk?
Answers
Answer:
width of the sidewalk = 1 feet
Step-by-step explanation:
Area of the pool = length × width
Length = 10 feet
Width = 6 feet
Area of the pool = length × width
= 10 feet × 6 feet
= 60 feet²
Area of the pool = 60 feet²
Total area = Area of the pool + Area of sidewalk
96 feet² = 60 feet ² + Area of sidewalk
Area of sidewalk = 96 feet² - 60 feet ²
Area of sidewalk = 36 feet²
Length of pool + sidewalk = 10 + 2x
width of pool + sidewalk = 6 + 2x
( 10 + 2 x ) ( 6 + 2 x ) -60 = 36
60 + 20x + 12x + 4x² - 60 = 36
4x² + 32x - 36 = 0
4x² + 36x - 4x - 36 = 0
4x (x + 9) -4(x + 9) = 0
(4x - 4) (x + 9) = 0
4(x - 1) (x + 9) = 0
(x - 1) = 0 (x + 9) = 0
x = 1 or x = -9
The width of the side walk can't be a negative value
Therefore, width of the sidewalk = 1 feet
A rectangular pool has a sidewalk around it. Width of the sidewalk is 1 feet.
Given
A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet.
Let 'w' be the width of sidewalk
The pool measures 6 feet by 10 feet . The width of the rectangular pool with side walk is 6+x+x=6+2x
The length of the rectangular pool with side walk is 10+2x
The total area of the pool and side walk is length times width
Total area= [tex](6+2x)(10+2x)\\[/tex]
[tex]96=(6+2x)(10+2x)\\96=60+32x+4x^2\\60+32x+4x^2-96=96-96\\4x^2+32x-36=0[/tex]
apply quadratic formula to solve for x
[tex]x=\frac{-32\pm \sqrt{32^2-4\cdot \:4\left(-36\right)}}{2\cdot \:4}\\x=\frac{-32\pm \:40}{2\cdot \:4}\\x= \frac{-32+40}{2\cdot \:4}=1\\x=\frac{-32-40}{2\cdot \:4}=-9[/tex]
Width of the sidewalk cannot be negative
so the width of the sidewalk is 1 feet
Learn more : brainly.com/question/21860114
18. Write an equation in point-slope form of the line that passes through the given point and with the given slope m.
(-3,1);m=3
20. Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(-3,-5);y=-2x+2
21. Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(0,0);y=-3x+2
Answers
Answer:
(-4,-2); y=4x+2
Step-by-step explanation:
The Bailey’s spent $18.00 for 4 two-liter sodas for the birthday party this weekend. What is the number of soda bottles that could be bought for $45.00?
Answers
Answer:
10
Step-by-step explanation:
So I belive the answer consists of- 18 divided by 4 equals 4.5 and 45 divided by 4.5 is 10 so ten should be your answer.
At a day care center a researcher asks children to list their five favorite toys from most favorite to least favorite. What level of measurement is represented in this example
Answers
Answer:
Ordinal
Step-by-step explanation:
The ordinal measurement level means the arrangement of the number so that it could tell the position of something in the list
Since in the question it is mentioned that the day care center ask the children for listing their five favorite toys and the arrangement could be done from most favorite to least favorite
So this represent the ordinal measurement level
It took Sheldon 17 5/6 minutes to walk to Raj's house. The bus ride home took Sheldon 4 5/8 minutes. How many more minutes did it take Sheldon to walk than to take the bus?
Answers
Answer:
it will take her [tex]13\frac{5}{24}[/tex] minutes more to walk down to Raj's House
Step-by-step explanation:
It took Sheldon [tex]17 \frac{5}{6}[/tex] minutes to walk to Raj's house
It also took Sheldon [tex]4\frac{5}{8}[/tex] minutes to use the bus.
To get the time difference between the two transport mechanisms, we subtract their different time durations.
This will be
[tex]17\frac{5}{6} - 4\frac{5}{8}=317/24[/tex]
We can convert this to Mixed fractions as shown [tex]13\frac{5}{24}[/tex] minutes.
Therefore, it will take her [tex]13\frac{5}{24}[/tex] minutes more to walk down to Raj's House
GIVING BRAINLIEST FOR CORRECT ANSWER!!!!
Answers
Answer:
All systems have 2 real solutions.
Step-by-step explanation:
there are X and Y unknowns.
What is 2/5 ÷ 3 and 1/10
Answers
Answer:
0.13 and 0.1 hope it will help you..
Steve gets 4 points for every correct answer and loses 1 point for every wrong answer. If he answered 30 questions and scored 20 points, write a system of equations.
Answers
Given:
Steve gets 4 points for every correct answer and loses 1 point for every wrong answer.
Total question answered by Steve = 30
Total score = 20 points
To find:
The system of equations for the given problem.
Solution:
Let x be the number of correct answers and y be the number of wrong answers.
Total question answered by Steve = 30
[tex]x+y=30[/tex] ...(i)
Steve gets 4 points for every correct answer and loses 1 point for every wrong answer.
Score for 1 correct answer = 4
Score for x correct answer = 4x
Score for 1 wrong answer = -1
Score for y correct answer = -y
Total score = 20 points
[tex]4x-y=20[/tex] ...(ii)
The system of equations contains (i) and (ii).
Therefore, the system of equations have two equations [tex]x+y=30[/tex] and [tex]4x-y=20[/tex].
19. The numerator of a fraction is 1 less than the denominator.
When both numerator and denominator are increased by 2,
the fraction is increased by 1/12Find the original fraction.
Answers
Let the original fraction be
[tex]\dfrac{n-1}{n}[/tex]
Now let's increase both numerator and denominator by 2:
[tex]\dfrac{n+1}{n+2}[/tex]
This produces a 1/12 increase:
[tex]\dfrac{n+1}{n+2}-\dfrac{n-1}{n}=\dfrac{1}{12}[/tex]
The left hand side can be rearranged as
[tex]\dfrac{2}{n^2+2n}=\dfrac{1}{12}[/tex]
Invert both sides:
[tex]\dfrac{n^2+2n}{2}=12 \iff n^2+2n=24[/tex]
Solve the quadratic equation:
[tex]n^2+2n-24=0 \iff n=-6 \lor n=4[/tex]
So, in the first case, the original fraction is
[tex]\dfrac{n-1}{n}=\dfrac{-6-1}{-6}=\dfrac{7}{6}[/tex]
In the second case, we have
[tex]\dfrac{n-1}{n}=\dfrac{4-1}{4}=\dfrac{3}{4}[/tex]
Find the value of x in the parallelogram.
Answers
Answer:
Since it's a parallelogram, the length of AD and BC are the same.
Hence, [tex]x + 21 = 12x - 1[/tex].
[tex]x + 21 = 12x - 1[/tex]
[tex]12x - x = 21 + 1[/tex]
[tex]11x = 22[/tex]
[tex]x = 2[/tex]
Therefore, x = 2.
Step-by-step explanation:
Hope this helped!
what is the answer. can someone help me .
Answers
Answer:
your photo is not visible for me
Answer:
54
Step-by-step explanation:
11x=26=180
x=14
8x+p+14=180
p=54
Which is the fraction 14/5 written as a mixed number
Answers
Or
Two and four fifths
baseball fans can buy tickets for seats in the lower deck or upper deck of the stadium. Tickets for the lower deck cost $42 each. Tickets prices for the upper deck are 75% of the cost of tickets for the lower deck. Which inequality represents all possible combinations of x, the number of tickets for the lower deck, and y the number of tickets for the upper deck, that someone can buy for no more than $800?
A.) 42x + 56y < 800
B.) 42x + 56y > 800
C.) 42x + 31.5y > 800
D.) 42x + 31.5y < 800
Answers
Answer:
b
Step-by-step explanation:
Answer:
the answer is D
What is 16 divided by 5
Answers
Answer:
3.2
Step-by-step explanation:
Henry's potato vine is growing like crazy! When he planted it, it was 2 inches long. Two weeks later it was 5 inches long. At 6 weeks, it was 11 inches long.
Answers
Answer:
[tex]y = \frac{3}{2}x +2[/tex]
Step-by-step explanation:
Required:
Write an equation to represent this situation
Let x represents the number of weeks and y represents the growth.
When he planted it:
[tex](x_1,y_1) = (0,2)[/tex]
Two weeks later:
[tex](x_2,y_2) = (2,5)[/tex]
At 6 weeks:
[tex](x_3,y_3) = (6,11)[/tex]
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{5-2}{2-0}[/tex]
[tex]m = \frac{3}{2}[/tex]
Then calculate the equation using:
[tex]y - y_3 = m(x - x_3)[/tex]
[tex]y - 11 = \frac{3}{2}(x - 6)[/tex]
[tex]y - 11 = \frac{3}{2}x - 9[/tex]
Solve for y
[tex]y = \frac{3}{2}x - 9+11[/tex]
[tex]y = \frac{3}{2}x +2[/tex]
whats the answeer giving brainliest
Answers
Answer:
B
Step-by-step explanation:
3+5+7=3+7+5
Who's ur favorite song artist?
Answers
The screen on Brianna's new phone is 2.65 cm. Long. What mixed number represents the length of the phone screen ?
Answers
Answer:
2 13/20 cm
Step-by-step explanation:
The screen on Brianna's new phone is 2.65 cm. Long. What mixed number represents the length of the phone screen ?
From the above question, we are converting, from decimal to mixed number , hence:
2.65 has 2 decimal places
Hence:
2.65 cm = (265/100)cm
= ( 2 + 65/100) cm
= ( 2 13/20 )cm
The mixed number that represents the length of the phone screen is 2 13/20 cm
As a cold front moved into a city, the temperature decreased by 32°F at a rate of
2°F per minute. For how long was the temperature decreasing?
A 64 minutes
B 30 minutes
C 32 minutes
D 16 minutes
Answers
Answer:
D. 16
Step-by-step explanation:
32/2 = 16