Quiz about Parent Function Transformations

Question 1

Which parent function is defined by

$$f\left(x\right)\ =\ 2^x$$

Accepted Answer

Exponential

Answer

Quadratic

Answer

Cubic

Answer

Square root

Question 2

What parent function has been transformed in

$$f\left(x\right)\ =\ \frac{1}{2}\sqrt[2]{x\ -\ 3}\ +\ 5$$

Accepted Answer

Square root

Answer

Linear

Answer

Cubic

Answer

Quadratic

Question 3

Which equation is a cubic function reflected across the x -axis, shifted right 2 units and down 4 units?

Accepted Answer

$$f\left(x\right)\ =\ -\left(x\ -2\right)^3\ -\ 4$$

Answer

$$f\left(x\right)\ =\ -\left(x-2\right)^2\ -\ 4$$

Answer

$$f\left(x\right)\ =\ -\left|x\ +2\right|\ +\ 4$$

Answer

$$f\left(x\right)\ =\ 2^{-\left(x\ -\ 2\right)}\ +\ 4$$

Question 4

Describe the parent function and the transformations of

$$g\left(x\right)\ =\ 2^{4\left(x-6\right)}\ $$

Accepted Answer

Exponential vertically stretched by a factor of 4 and shifted right 6 units

Answer

Exponential shifted right 6 units and up 4 units

Answer

Exponential vertically compressed by a factor of 4 and shifted right 6 units

Answer

Quadratic vertically stretched by a factor of 4 and shifted right 6 units

Question 5

Write an equation for the functions shown in the graph

Accepted Answer

$$f\left(x\right)\ =\ \sqrt[2]{x\ -\ 1}\ +\ 2$$

Answer

$$f\left(x\right)\ =\ 2^{x\ -1}\ +\ 2$$

Answer

$$f\left(x\right)\ =\ \left(x\ -1\right)^3\ +\ 2$$

Answer

$$f\left(x\right)\ =\ \left|x-1\right|+\ 2$$

Question 6

Which parent function is graphed heer?

Accepted Answer

Absolute Value

Answer

Exponential

Answer

Linear

Answer

Quadratic

Question 7

Question 7.

Accepted Answer

y = -Ix + 2I - 1

Answer

y = Ix + 2I - 1

Answer

y = -Ix - 2I - 1

Answer

y = -Ix + 1I - 2

Question 8

Describe the transformation from the parent graph

Accepted Answer

Reflect over x, right 3, down 4

Answer

Reflect over y, right 3, down 4

Answer

Reflect over x, right 3, up 4

Answer

Reflect over y, left 3, down 4

Question 9

Match 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

Question 10

Describe the transformations from the original parent function f(x) = x².
g(x) = 5x² + 2

Accepted Answer

Vertical Stretch of 5
Up 2

Answer

Vertical Stretch of 5
Down 2

Answer

Vertical Shrink of 5
Up 2

Answer

Vertical Shrink of 5
Down 2

Question 11

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 12

Which parent function is shaped like the letter v?

Accepted Answer

absolute value

Answer

square root

Answer

cubic

Answer

exponential

Question 13

Describe the transformations and the parent function

Accepted Answer

Cubic reflected across x, shifted right 2 units and up 1 unit

Answer

Quadratic shifted right 2 and down 3

Answer

Square root reflected across x, shifted right 2 units and up 1 unit

Answer

Exponential shifted right 2 units and up 1 unit

Question 14

What is the equation of the PARENT  function?

Accepted Answer

f(x) = x3

Answer

f(x) = 2x

Answer

f(x) = |x|

Answer

f(x) = x

Question 15

g(x)=f(x+5)
Describe the transformation to f(x) that results in g(x).

Accepted Answer

f(x) has been translated to the left 5.

Answer

f(x) has been translated to the right 5.

Parent Function Transformations

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