Question 1

Which of the following describes the effect of the transformation $$y = f(x) + 4 on $$the graph of $$y = f(x)$$?

Accepted Answer

The graph shifts 4 units upward.

Question 2

Given $$f(x) = x^2$, what is the equation of the graph that results from reflecting f(x$$)$$ about the x-axis and then shifting it down by 3 units?

Accepted Answer

$$y = -x^2$ - 3$$

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = |x|$$

Question 4

If $$f(x) = |x|$$, which transformation produces the graph of $$y = |x - 2|$$?

Accepted Answer

Shift the graph 2 units to the right.

Question 5

Which of the following describes the transformation from $$y = f(x) to$$ $$y = f(-x)$$?

Accepted Answer

Reflection about the y-axis

Question 6

Suppose $$f(x) = x^2$. What is the effect of the transformation y = 3f(x$$)$$?

Accepted Answer

The graph is vertically stretched by a factor of 3.

Question 7

Which of the following is the domain of the square root function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 8

A company models its profit with $$P(x) = |x - 5|. $$What does the transformation $$P(x) = |x - 5| + 2$$ represent in the context of the graph?

Accepted Answer

The profit graph shifts 2 units upward.

Question 9

Given $$f(x) = x^3$, what is the effect of the transformation y = f(2x$$)$$?

Accepted Answer

The graph is horizontally shrunk by a factor of 2.

Question 10

Which of the following is true about the function $$f(x) = x^3$?

Accepted Answer

It is an odd function.

Question 11

If $$f(x) = x^2$, what is the equation for the graph that is shifted 3 units to the left and 2 units up?

Accepted Answer

$$y = (x + 3)^2$ + 2$$

Question 12

Which transformation will change the graph of $$y = f(x) to$$ $$y = -2f(x)$$?

Accepted Answer

Reflect about the x-axis and vertically stretch by 2.

Question 13

Which of the following is the range of the absolute value function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 14

A medical researcher models the spread of a virus with $$N(t) = \sqrt{t}$$, where $$t is $$days since exposure. What is the effect of the transformation $$N(t) = 2\sqrt{t}$$?

Accepted Answer

The graph is vertically stretched by a factor of 2.

Question 15

Which transformation sequence will produce the graph of $$y = -\frac{1}{2}(x + 1)^2$ - 2$$ from $$y = x^2$?

Accepted Answer

Shift left 1, shrink vertically by $$\frac{1}{2}$$, reflect about the x-axis, shift down 2.

Question 16

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

Accepted Answer

$$(-\infty, \infty)$$

Question 17

If $$f(x) = x$$, what is the effect of the transformation $$y = f(x) - 5$$?

Accepted Answer

The graph shifts 5 units downward.

Question 18

Which of the following best describes the transformation from $$y = f(x) to$$ $$y = f(\frac{1}{2}x)$$?

Accepted Answer

Horizontal stretch by a factor of 2.

Question 19

A city models its population growth with $$P(t) = t^2$. What is the effect of the transformation P(t) = (t$$ - $$10)^2$$?

Accepted Answer

The graph shifts 10 units to the right.

Transformations of Functions: College Algebra Study Notes

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