Question 1

Which transformation is illustrated by the change from $$f(x) = |x| to$$ $$g(x) = 2|x| as $$shown in the first image?

Accepted Answer

A vertical stretch by a factor of 2

Question 2

Given the graph of $$f(x) = |x|$$, what transformation produces $$h(x) = \frac{1}{2}|x| as $$shown in the second image?

Accepted Answer

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

Question 3

Which transformation is shown in the third image, comparing $$f(x) = \sqrt{x}$$ and $$g(x) = -\sqrt{x}$$?

Accepted Answer

Reflection across the x-axis

Question 4

In the fourth image, $$h(x) = \sqrt{-x} is $$shown. What transformation has been applied to $$f(x) = \sqrt{x} to $$obtain $$h(x)$$?

Accepted Answer

Reflection across the y-axis

Question 5

Which type of symmetry does the graph $$y = x^2$ + 4 ($$fifth image) exhibit?

Accepted Answer

Symmetry with respect to the y-axis

Question 6

The graph in the sixth image shows a line with no x-axis or y-axis symmetry. Which of the following is true about this graph?

Accepted Answer

It is neither even nor odd

Question 7

In the seventh image, $$g(x) = |x| - 4 is $$shown. What transformation has been applied to $$f(x) = |x|$$?

Accepted Answer

Vertical translation 4 units down

Question 8

Which transformation is illustrated in the eighth image by the change from $$y = f(x) to$$ $$y = f(x) + 2$$?

Accepted Answer

Vertical translation 2 units up

Question 9

In the ninth image, $$g(x) = |x - 4| is $$shown. What transformation has been applied to $$f(x) = |x|$$?

Accepted Answer

Horizontal translation 4 units right

Question 10

Which transformation is shown in the tenth image by the change from $$y = f(x) to$$ $$y = f(x + 2)$$?

Accepted Answer

Horizontal translation 2 units to the left

Question 11

Given $$f(x) = -|x + 3| + 1 as $$shown in the eleventh image, which sequence of transformations is correct?

Accepted Answer

Shift left 3 units, reflect across x-axis, shift up 1 unit

Question 12

The graph $$g(x) = -\frac{1}{2}x^2$ + 4 ($$twelfth image) is obtained from $$f(x) = x^2$ by which transformations?

Accepted Answer

Vertical stretch by $$\frac{1}{2}$$, reflection across x-axis, shift up 4 units

Question 13

If $$y = f(x) is $$shown in the thirteenth image, what transformation produces $$g(x) = f(x) + 3 as in $$the fourteenth image?

Accepted Answer

Vertical translation 3 units up

Question 14

Given $$y = f(x) in $$the thirteenth image, what transformation produces $$h(x) = f(x + 3) as in $$the fifteenth image?

Accepted Answer

Horizontal translation 3 units left

Question 15

Given $$y = f(x) in $$the thirteenth image, what transformation produces $$k(x) = f(x - 2) + 3 as in $$the sixteenth image?

Accepted Answer

Horizontal translation 2 units right and vertical translation 3 units up

Question 16

Given $$y = f(x) in $$the thirteenth image, what transformation produces $$F(x) = -f(x) as in $$the seventeenth image?

Accepted Answer

Reflection across the x-axis

Question 17

Which of the following statements is TRUE about the symmetry of even and odd functions?

Accepted Answer

Even functions are symmetric with respect to the y-axis.

Question 18

Suppose $$f(x) is an $$odd function. Which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(-x) = -f(x)$$

Graphing Techniques in College Algebra: Transformations, Symmetry, and Function Properties

Study Guide - Practice Questions