Quiz about Transforming Functions

Question 1

Describe the transformation of y = f(x) for the new function
y = f(x) - 5

Accepted Answer

The graph of y = f(x) was shifted down 5 units.

Answer

The graph of y = f(x) was shifted to the right 5 units.

Answer

The graph of y = f(x) was shifted to the left 5 units.

Answer

The graph of y = f(x) was shifted up 5 units.

Question 2

Which equation describes the transformation of shifting f(x)=x² two units right?

Accepted Answer

f(x - 2)

Answer

f(x) + 2

Answer

f(x) - 2

Answer

f(x + 2)

Question 3

What are the transformations from the parent function y=x²?

y=3(x-4)²?

Accepted Answer

vertical stretch by a factor of 3, horizontal shift right by 4

Answer

horizontal shift left by 4, vertical stretch by a factor of 3

Answer

horizontal shift right by 4, vertical stretch by a factor of 1/3

Answer

horizontal shift right by 4, vertical shift up 3

Question 4

Describe the transformation of y = f(x) for the new function
f(x) = 5x² + 2

Accepted Answer

Stretch of 5
Up 2

Answer

Shrink of 5
Up 2

Answer

Stretch of 5
Down 2

Answer

Shrink of 5
Down 2

Question 5

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

Accepted Answer

Right 3 and up 5

Answer

Left 3 and up 5

Answer

Right 3 and down 5

Answer

Left 3 and down 5

Question 6

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

Accepted Answer

-f(x)

Answer

f(-x)

Answer

f-1(x)

Answer

f(2x)

Question 7

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

Accepted Answer

g(x)=(x-1)³

Answer

g(x)=x3+1

Answer

g(x)=x3-1

Answer

g(x)=(x+1)³

Question 8

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

Accepted Answer

g(x) = f(x - 1)

Answer

g(x) = f(x) + 1

Answer

g(x) = f(x) - 1

Answer

g(x) = f(x + 1)

Question 9

Identify the transformation from the graph of f(x)=x²to the graph g(x)= -(x+5)²

Accepted Answer

shifted left 5 units
reflection x-axis

Answer

shifted up five units
reflection in x-axis

Answer

shifted down five units
reflection in x-axis

Answer

shifted right 5 units
reflection x-axis

Question 10

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

Accepted Answer

(-6, 5)

Answer

(-2, 5)

Answer

(-4, 3)

Answer

(-4, 7)

Question 11

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = -f(x - 2) - 3 , what is the vertex of g(x)?

Accepted Answer

(-2, -8)

Answer

(-6, -8)

Answer

(-2, 2)

Answer

(-2, -2)

Question 12

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x - 2) - 3 , what is the vertex of g(x)?

Accepted Answer

(-2, 2)

Answer

(-6, 8)

Answer

(-2, 8)

Answer

(-6, 2)

Question 13

Describe the transformations that maps (order matters)

y = g(x) to y = - g(x + 6) - 10

Accepted Answer

Reflect over x-axis

Shifted down 10 units

Shifted left 6 units

Answer

Shifted down 10 units

Shifted right 6 units

Reflect over x-axis

Answer

Reflect over x-axis

Shifted down 10 units

Shifted right 6 units

Answer

Shifted down 10 units

Shifted left 6 units

Reflect over x-axis

Question 14

(Order matters) Select all possible combinations that correctly transforms:

y = g(x) to y = - 2g(x + 6) - 10

Accepted Answer

Reflect over x-axis

Vert stretch by 2

Shifted down 10 units

Shifted left 6 units

Accepted Answer

Vert stretch by 2

Reflect over horizontal axis

Shifted down 10 units

Shifted left 6 units

Accepted Answer

Reflect over x-axis

Vert stretch by 2

Shifted left 6 units

Shifted down 10 units

Answer

Shifted down 10 units

Shifted left 6 units

Reflect over x-axis

Vert stretch by 2

Question 15

If the blue is f(x)=x^2,then the red must be ___?

Accepted Answer

g(x) = f(x) - 5

Answer

g(x )= f(x) + 5

Answer

g(x) = f(x - 5)

Answer

g(x) = f(x + 5)

Question 16

. If the blue is f(x)=x^2,then the red must be ___?

Accepted Answer

g(x)=x2-5

Answer

g(x)=x2+5

Answer

g(x)=(x-5)²

Answer

g(x)=(x+5)²

Question 17

Describe the transformation of y = f(x) to the new function
y = f(1/5x)

Accepted Answer

Horizontal stretch by a factor of 5

Answer

Horizontal shrink by a factor of 1/5

Answer

Vertical stretch be a factor of 5

Answer

Vertically shrink by a factor of 1/5

Question 18

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

Accepted Answer

f(x - 3)

Answer

f(x + 3)

Answer

f(x) + 3

Answer

f(x) - 3

Question 19

If the original graph is f(x), and the new graph has been moved two to the left, what would be the new graph in f(x) notation?

Accepted Answer

f(x + 2)

Answer

f(x) + 2

Answer

f(x - 2)

Answer

f(x) - 2

Question 20

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

Accepted Answer

f(x - 4) + 3

Answer

f(x + 3) - 4

Answer

f(x + 4) + 3

Answer

f(x + 3) + 4

Question 21

.
If the blue is f(x)=x^2,the red must be

Accepted Answer

g(x)=(x-3)²

Answer

g(x)=(x+3)²

Answer

g(x)=x2+3

Answer

g(x)=x2-2

Question 22

Which of the following transformations are present?
-2f(x - 1) + 2

Accepted Answer

Shift 1 unit right

Answer

Shift 1 unit down

Answer

Shift 1 unit up

Answer

Shift 1 unit left

Question 23

Which of the following transformations are present (select all that apply)?

-2f(2(x - 1)) + 2

Accepted Answer

vertical shift

Accepted Answer

reflection over horizontal axis

Accepted Answer

horizontal compression

Answer

reflection over vertical axis

Answer

Rotation about origin

Question 24

Describe the transformation that occurred

h(x) = 1/5f(x)

Accepted Answer

vertical compression by 5

Answer

vertical stretch by 5

Answer

vertical translation by 5

Answer

vertical translation by -5

Question 25

Identify the transformation from the graph of f(x)=2^xto the graph g(x)=2^x-3

Accepted Answer

vertical translation by -3

Answer

horizontal translation right by 3

Answer

vertical translation by 3

Answer

horizontal translation left by 3

Question 26

Order the functions from the narrowest graph to widest.

f(x) = 1/2x²

g(x) = -3x²

h(x) = x²

Accepted Answer

g(x), h(x), f(x)

Answer

f(x), g(x), h(x)

Answer

f(x), h(x), g(x)

Answer

h(x), f(x), g(x)

Question 27

If f(x) = x², order the following graphs from narrowest (first) to widest (last): f(x), f(2x), f(0.5x), f(3x)

Accepted Answer

f(3x), f(2x), f(x), f(0.5x)

Answer

f(0.5x), f(x), f(2x), f(3x)

Answer

f(3x), f(2x), f(0.5x), f(x)

Answer

f(x), f(2x), f(3x), f(0.5x)

Question 28

Which transformations of f(x) with stretch the graph vertically or horizontally (select all that apply)?

Accepted Answer

3f(2(x - 1)) + 4

Accepted Answer

f(2(x-5))+1

Accepted Answer

3f(x) + 2

Accepted Answer

f(0.5x) + 1

Answer

-f(x - 2) +3

Question 29

When transforming the function y = g(x) to the function

y = 3g(x - 3) + 5, which transformations should be performed last (select all that apply)?

Accepted Answer

horizontal translation right 3

Accepted Answer

vertical translation up 5

Answer

vertical stretch by 3

Answer

horizontal translation left 3

Answer

reflection over horizontal axis

Question 30

Describe the order of transformations from the parent function g(x) =1/x, to f(x).

Accepted Answer

reflection over the x-axis, horizontal translation by 2, vertical translation by 4

Answer

horizontal translation by 2, vertical translation by 4

Answer

reflection over the y-axis, horizontal translation by 2, vertical translation by 4

Answer

horizontal translation by 2, vertical translation by 4, reflection over the x-axis

Question 31

What is the equation of this graph?

Accepted Answer

f(x) = -2(x - 1)² + 3

Answer

f(x) = -2(x + 1)² + 3

Answer

f(x) = -2(x + 1)² - 3

Answer

f(x) = -2(x - 1)² - 3

Question 32

What is the equation of this graph?

Accepted Answer

f(x) = |x - 2| - 2

Answer

f(x) = (x + 2)² - 2

Answer

f(x) = (x - 2)² - 2

Answer

f(x) = |x + 2| - 2

Question 33

What type of function is shown?

Accepted Answer

Square root

Answer

Cube root

Answer

Quadratic

Answer

Exponential

Question 34

What type of function is shown?

Accepted Answer

linear

Answer

absolute value

Answer

quadratic

Answer

exponential

Question 35

Name the parent function.

Accepted Answer

square root

Answer

linear

Answer

cubic

Answer

exponential

Question 36

Name the parent function.

Accepted Answer

cubic

Answer

linear

Answer

quadratic

Answer

cube root

Question 37

Name the parent function.

Accepted Answer

exponential

Answer

square root

Answer

quadratic

Answer

cubic

Question 38

What is the equation for the red function?

Accepted Answer

g(x)=(x-1)³

Answer

g(x)=x3+1

Answer

g(x)=x3-1

Answer

g(x)=(x+1)³

Question 39

The blue is f(x)=|x|, red must be

Accepted Answer

g(x)=|x-2|

Answer

g(x)=|x+2|

Answer

g(x)=|x|+2

Answer

g(x)=|x|-2

Question 40

What is the name of this function?

Accepted Answer

Rational Function

Answer

Parabola

Answer

Ellipse

Answer

Cubic

Question 41

What type of function is shown?

Accepted Answer

absolute value

Answer

linear

Answer

quadratic

Answer

square root

Question 42

What type of function is shown?

Accepted Answer

quadratic

Answer

cube root

Answer

absolute value

Answer

square root

Question 43

What type of function is shown?

Accepted Answer

exponential

Answer

logarithm

Answer

quadratic

Answer

square root

Question 44

What type of function is shown?

Accepted Answer

cube root

Answer

Exponential

Answer

square root

Answer

quadratic

Question 45

Describe the parent graph transformation

Accepted Answer

compression by 1/2, left 1, down 3

Answer

stretch by 1/2, left 1, down 3

Answer

stretch by 1/2, right 1, down 3

Answer

compression by 1/2, right 1, down 3

Question 46

What shifts have occurred?

Accepted Answer

right 1, up 5

Answer

left 1, up 5

Answer

left 1, down 5

Answer

right 1, down 5

Question 47

Math the equation with the graph:

Accepted Answer

y = -(x - 2)² + 4

Answer

y = (x - 2)² + 4

Answer

y = -(x - 4)² + 2

Answer

y = -(x + 2)² + 4

Transforming Functions

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