Question 1 of 10
Which function results after applying the sequence of transformations to
f(x) = x5?
• shift left 1 unit
• vertically compress by
3
• reflect over the y-axis
Answers
Answer: B) [tex]f\left(x\right)=\frac{1}{3}\left(-x-1\right)^{5}[/tex]
Step-by-step explanation:
When graphing x5 the parent function and plugging in the equation for B the only equation that fits the criteria of
*shifting left 1 unit
*vertically compressed by 1/3
*reflect over the y-axis
So the answer is B
The function after the transformation is f ( x ) = ( 1/3 ) ( -x + 1 )⁵
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x⁵
On reflecting over the y axis , we get
f ( x ) = ( -x )⁵
On vertically compressing by a factor of ( 1/3 ) , we get
f ( x ) = ( 1/3 ) ( -x )⁵
And , shifting 1 unit to the left , we get
f ( x ) = ( 1/3 ) ( -x + 1 )⁵
Hence , the transformed function is f ( x ) = ( 1/3 ) ( -x + 1 )⁵
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Related Questions
hshsjshshsjsksjjsbsbbs bc hd
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Answer:
its b b b
Step-by-step explanation:
find the estimates for the following:
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Answer:
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Step-by-step explanation:
Helppppp and explain pls and thankyouuu
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Answer: B
Step-by-step explanation:
multiply all the the sales by 11% and you will get the answers in option b
ex: 1300*0.11=143
A house plan Is drawn to a scale 1cm to 2m. What is the length of a window 2.5cm long on the plan?
Answers
1cm = 2m
=> 1cm = 200cm
2.5cm = 2.5 × 200cm = 500 cm = 5m
So, the length of window is 500cm or 5m.
PLEASE SHOW ALL WORK
The function s(t) = t2+2t+5shows the height s(t), in feet, of a water balloon after t seconds. A second water balloon moves in the air along a path represented by p(t)=11+3t where p(t) is the height, in feet, of the balloon from the ground at time t seconds.
Part A: Create a table using integers 1 through 4 for the two functions. What is the solution for s(t) = p(t)? How do you know? Include the table in your answer.
Part B: Explain what the solution from Part A means in context of the problem.
Answers
Answer:
t = 2,3
Step-by-step explanation:
s (t) = t^2 + 2 t + 5
p (t) = 11 + 3 t
A:
s (1) = 8
s (2) = 13
s (3) = 20
s (4) = 29
Now
[tex]t^2 + 2 t + 5 = 11 t + 3t \\\\t^2 - t - 6 = 0\\\\t^2 - 3 t - 2 t - 6 = 0 \\\\(t-2)(t-3)=0\\\\t = 2, 3[/tex]
(b) The values are same at t =2 an t =3.
Please help me with this
Answers
Answer:
52 in^2
Hope this helps!
What is the gradient of a line perpendicular to a line with a gradient of -6?
Answers
Answer:
1/6
Step-by-step explanation:
Gradient of a line perpendicular to a line with a gradient of m = -1/m
Gradient of a line perpendicular to a line with a gradient of -6 = -1 /-6 = 1/6
What is the difference between calculating the area and calculating the perimeter of a rectangle?
Answers
Answer:
For perimeter you add up the side lengths to get the perimeter but for area you multiply the length times width (L x W )to get area.
Step-by-step explanation:
PLEASE HELP, I WILL GIVE YOU BRAINLIEST!
Find the equation of a line that results in one real solution as part of a system with f(x)=x^2+2
Answers
Step-by-step explanation:
i hope this will help you
Answer:
give that person brainliest
Step-by-step explanation:
I am tired bestie. You are lucky we are friends. want sleep but homeworrkkk
WILL GIVE BRAINLIST!
What is the slope of the line graphed on the coordinate plane?
A graph with a line running through coordinates (0, 6) and coordinates (1, -2)
Answers
Work Shown:
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (-2-6)/(1-0)
m = -8/1
m = -8
The slope is -8
We can think of it like saying "go down 8 and move to the right 1 unit", since -8 = -8/1.
Put another way: slope = rise/run = -8/1
rise = -8 and run = 1.
Answer:
-8
it's easy just use the equation y2-y1 ÷ x2-x1
Which expression is equivalent to 5g+9+8g+4?
Answers
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{5g + 9 + 8g + 4}\\\\\huge\textsf{COMBINE the LIKE TERMS}\\\\\large\textsf{5g + 8g + 9 + 4}\\\\\large\textsf{5g + 8g = \bf 13g}\\\\\large\textsf{9 + 4 = \bf 13}\\\\\boxed{\huge\textsf{= 13g + 13}}\large\checkmark\\\\\\\\\\\\\boxed{\boxed{\huge\textsf{Answer: \bf 13g + 13}}}\huge\checkmark\\\\\\\\\\\\\\\\\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
Graph the function F(x)=2^x-4
Answers
Answer:
The plotting are correct .
HOPE IT HELPED!!
h(x) = -4x – 7, when x = 3:
Answers
h(3)= -12-7
h(3)= -19
.•. h(3) = -19
Answer:
h(x) = -4 x –7
h(3) = -4(3) —7
h(3) = –12 –7
h(3) = – 19
Which of the following is not a proportional liner relationship?
Answers
=========================================================
Explanation:
A proportional linear relationship is of the form y = kx
We can solve for k to get k = y/x.
Based on that, we can prove a table is a proportional linear relationship if and only if each column of x,y values divide to the same number.
Choice A shows that y/x = 2/8 = 1/4 for the first column; however, y/x = 8/16 = 1/2 for the second column. The outputs 1/4 and 1/2 not being the same indicates we don't have a constant k value for all of the columns. This is sufficient to show that table A is not a proportional linear relationship.
-------------
In contrast, table B is a proportional linear relationship because we have these four divisions that lead to the same value (1/8)
Column One: y/x = 2/16 = 1/8Column Two: y/x = 4/32 = 1/8Column Three: y/x = 6/48 = 1/8Column Four: y/x = 8/48 = 1/8Showing that k = 1/8 for table B. The equation here is y = (1/8)x. We can rule out choice B.
I'll let you check out tables C and D on your own, but you should find that a similar situation shows up as did with table B. This indicates tables C and D are also proportional linear relationships. We can rule out choices C and D.
Solve for x. Round to the nearest tenth, if necessary.
Answers
CoS61X
5.5=* (Cos (60)
11.344
-
X= 5.5
COSC61)
The answer is in the picture
Solve for x. Round to the nearest tenth, if necessary.
Answers
Sin(41 deg) = 2.5/x
Xsin(41) = 2.5
X = 2.5/sin(41)
X = 3.8
Which of the following
is most likely the next step in the series?
Answers
Answer:
B.
Step-by-step explanation:
The numbers are always in the blue side, and the blue side starts at facing right, left, right, and then left.
which country won
the last world cup
Answers
Answer:
The country is France.
The correct answer is France
The probability that Caroline wins a raffle is given by the expression
m/n.
Write down an expression, in the form of a combined single fraction, for the probability that Caroline does not win.
Answers
Answer: [tex]\frac{n-m}{n}[/tex]
This is the same as writing (n-m)/n
Don't forget about the parenthesis if you go with the second option.
==================================================
Explanation:
The probability that she wins is m/n, where m,n are placeholders for positive whole numbers.
For instance, m = 2 and n = 5 leads to m/n = 2/5. This would mean that out of n = 5 chances, she wins m = 2 times.
The probability of her not winning is 1 - (m/n). We subtract the probability of winning from 1 to get the probability of losing.
We could leave the answer like this, but your teacher says that the answer must be "in the form of a combined single fraction".
Doing a bit of algebra would have these steps
[tex]1 - \frac{m}{n}\\\\\frac{n}{n} - \frac{m}{n}\\\\\frac{n-m}{n}\\\\[/tex]
and now the expression is one single fraction.
A square pyramid is inscribed in a rectangular prism. A cone is inscribed in a cylinder. The pyramid and the cone have the same volume. Part of the volume of the rectangular prism, 1 V 1 , is not taken up by the square pyramid. Part of the volume of the cylinder, 2 V 2 , is not taken up by the cone. What is the relationship of these two volumes, 1 V 1 and 2 V 2 ?
Answers
Answer:
V₂ = V₁
Step-by-step explanation:
Let the height of the rectangular prism = h
Let s represent the side length of the base of the square prism, we have;
The volume of the prism, [tex]V_{prism}[/tex] = s²·h
The volume of the square pyramid, [tex]V_{pyramid}[/tex] = (1/3)·s²·h
∴ V₁ = The area not taken up by the square pyramid = [tex]V_{prism}[/tex] - [tex]V_{pyramid}[/tex]
∴ V₁ = s²·h - (1/3)·s²·h = (2/3)·s²·h
Similarly, for the cylinder, we have;
Let h represent the height of the cylinder
Let r represent the radius of the base of the cone, we have;
Therefore;
The volume of the cylinder, [tex]V_{cylinder}[/tex] = π·r²·h
The volume of the cone, [tex]V_{cone}[/tex] = (1/3)·π·r²·h
∴ V₂ = π·r²·h - (1/3)·π·r²·h = (2/3)·π·r²·h
V₂ = (2/3)·π·r²·h
[tex]V_{cone}[/tex] = [tex]V_{pyramid}[/tex]
Therefore;
(1/3)·π·r²·h = (1/3)·s²·h
∴ π·r² = s²
Therefore, V₂ = (2/3)·π·r²·h = V₂ = (2/3)·s²·h = V₁
V₂ = V₁.
Set 2 Maths has 30 pupils in it.
Set 1 Maths has 80% of the number of pupils in Set 2
How many pupils does Set 1 Maths have?
Answers
Mark rolls a fair dice 48 times. How many times would Mark expect to roll a one?
Answers
Answer:
8 Times, Mark would expect to roll a one 'Eight times'
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
15.4 (rounded to 1dp)
Step-by-step explanation:
Use the elimination method to solve the system of equations.
A. Infinitely many solutions
B. (10, 10)
C. (16, 18)
D. No solution
Answers
Answer:
they are the dame line...
A. Infinitely many solutions
Step-by-step explanation:
The sum of two numbers is 50. The larger number is 20 more than the smaller number. What are the numbers?
Answers
Answer:
the smaller number is 15 and the larger number is 35
Step-by-step explanation:
x+y=50
x=smaller number y=larger number
y=x+20
x+(x+20)=50
2x+20=50
2x=30
x=15
smaller number=15
larger number= 15+20=35
Answer:
Smaller: 15
Larger: 35
Step-by-step explanation:
1. Finding the two equationsLarger: y
Smaller: x
[tex]x+y=50[/tex]
[tex]y=20+x[/tex]
2. Plugging it in[tex]x+20+x=50\\2x=50-20\\2x=30\\x=15[/tex]
[tex]15+y=50\\y=50-15\\y=35[/tex]
x=15; y=35
Hope this helped! Please mark brainliest :)
what is the length of KM ? no links . HELP
Answers
Answer:
40 units
Step-by-step explanation:
9x-5=7x+7
9x-7x=7+5
2x=12
x=6
6x+4
6(6)+4
36+4
40
At the baseball stadium there are 548 seats that are divided into 14 rows how many seats are in each row
Answers
Answer:
There are 39 seats I think.
Step-by-step explanation:
548 divided by 14 is a decimal but rounded it to the nearest full number.
− 0.32 + 0.18 = 0.25 − 1.95
Answers
Answer:
Step-by-step explanation:
0.18-0.32 = .25-1.95
-0.14 = 1.70
obviously that equation above is not true, I suspect that there were some "x" variables on some of those numbers?
identify the volume of a sphere if it has a surface area of 465 square units
Answers
Step-by-step explanation:
S.A = 465
4πr²= 465
r². = 36.9
r. = 6.08
volume of a sphere = 4/3πr³
= 4/3π * 6.08³
= 941.8 cm³
The radius of the sphere will be 6.08 units. Then the volume of the sphere will be 942.87 cubic units.
What is the volume of the sphere?A circular solid object or its surface whose points are all equally spaced from the center.
Let r be the radius of the sphere.
Then the volume of the sphere will be
V = 4/3 πr³ cubic units
The surface area of the sphere will be 465 square units.
The surface area of the sphere is given as,
SA = 4πr²
Then the radius of the sphere will be
4πr² = 465
r² = 37
r = 6.08 units
Then the volume of the sphere will be
V = 4/3 π (6.08)³
V = 4/3 π x 225.09
V = 300 π
V = 942.87 cubic units
Thus, the volume of the sphere will be 942.87 cubic units.
More about the volume of the sphere link is given below.
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what is the measure of 6 ?
Answers
Answer:
54°
Step-by-step explanation:
Here :-
13x + 9 + 5x + 9 = 1801 8x + 18= 180 18x = 162x = 9Measure of 6 :-
6 = 5x + 9 6 = 5*9 +9 6 = 45 + 9 6 = 54°Answer:
m<6 = m<2 = 54º
Step-by-step explanation:
13x + 9 + 5x + 9 = 180
18x + 18 = 180
18x = 180 - 18
18x = 162
x = 162 / 18
x = 9
13x + 9
13(9) + 9
126
180 - 126
54
m<6 = m<2 = 54º