Question 1

Which of the following describes the transformation that occurs to the graph of $$f(x) = x^2$ to obtain g(x$$) = $$(x-4)^2 + 2$?

Accepted Answer

Shift the graph 4 units to the right and 2 units up.

Question 2

Given $$f(x) = |x|$$, what is the effect of the transformation $$g(x) = -|x| on $$the graph of $$f(x)$$?

Accepted Answer

It reflects the graph about the x-axis.

Question 3

If $$f(x) = x^2$, which of the following is the graph of h(x$$) = $$3x^2$$?

Accepted Answer

A vertical stretch by a factor of 3.

Question 4

Which transformation will change $$f(x) = \sqrt{x} to$$ $$g(x) = \sqrt{x+5}$$?

Accepted Answer

Shift the graph 5 units to the left.

Question 5

Suppose $$f(x) = x^3$. What is the effect of the transformation g(x) = f(-x$$)$$?

Accepted Answer

Reflection about the y-axis.

Question 6

Given $$f(x) = x^2$, which function represents a horizontal shrink by a factor of 2?

Accepted Answer

$$f(2x) = (2x)^2$

Question 7

A medical imaging device uses the function $$f(x) = |x| to $$process signals. If the output is modified to $$g(x) = |x| - 4$$, what is the effect on the graph?

Accepted Answer

The graph is shifted 4 units down.

Question 8

Which of the following best describes the sequence of transformations for $$y = -2(x+1)^2$ + 3$$ starting from $$y = x^2$?

Accepted Answer

Shift left 1, vertical stretch by 2, reflect about x-axis, shift up 3.

Question 9

If $$f(x) = \sqrt{x}$$, what is the domain of $$g(x) = \sqrt{x-7}$$?

Accepted Answer

$$[7, \infty)$$

Question 10

A chemical reaction's rate is modeled by $$f(x) = x^3$. If the input is doubled, which function models the new rate?

Accepted Answer

$$f(2x) = (2x)^3$

Question 11

Which of the following is true about the function $$f(x) = x^2$?

Accepted Answer

It is an even function.

Question 12

Given $$f(x) = x^2$, what is the effect of the transformation g(x$$) = $$(x+3)^2 - 5$?

Accepted Answer

Shift 3 units left and 5 units down.

Question 13

If $$f(x) = \sqrt{x}$$, what is the effect of the transformation $$g(x) = 2\sqrt{x}$$?

Accepted Answer

Vertical stretch by a factor of 2.

Question 14

A population model uses $$f(x) = x^2$. If the model is changed to g(x$$) = \frac{1}{2}$$x^2$$, what is the effect?

Accepted Answer

Vertical shrink by a factor of $$\frac{1}{2}.$$

Question 15

Which transformation will change $$f(x) = x^2$ to g(x$$) = $$(x+2)^2$$?

Accepted Answer

Shift 2 units to the left.

Question 16

Given $$f(x) = x^3$, what is the effect of the transformation g(x$$) = $$-x^3$$?

Accepted Answer

Reflection about the x-axis.

Question 17

If $$f(x) = \sqrt{x}$$, which function represents a horizontal stretch by a factor of 3?

Accepted Answer

$$f(\frac{1}{3}x) = \sqrt{\frac{1}{3}x}$$

Question 18

A real-world scenario: The height of a projectile is modeled by $$f(x) = -x^2$ + 10. If $$the launch site is moved 3 units to the right, what is the new function?

Accepted Answer

$$f(x-3) = -(x-3)^2$ + 10$$

Question 19

Which of the following is true about the function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

It is an odd function.

Transformations of Functions: Precalculus Study Guide

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