Question 1

Given the function $$f(x) = x^2$, which of the following describes the transformation to obtain g(x$$) = $$-(x+2)^2 - 8$ from f(x$$)$$?

Accepted Answer

Reflect $$f(x)$$ over the $$x-$$axis, shift left 2 units, and down 8 units.

Question 2

Which of the following is the correct difference quotient for $$f(x) = 2x^2$?

Accepted Answer

$$\frac{2(x+h)^2$ - 2x^2$}{h}$$

Question 3

A function $$f is $$called even if:

Accepted Answer

$$f(-x) = f(x)$$ for all $$x in $$the domain of $$f$$

Question 4

Given the graph of $$f(x) = \sqrt{x}$$, which transformation results in the graph of $$g(x) = -\sqrt{x}$$?

Accepted Answer

Reflection about the $$x-$$axis

Question 5

What is the average rate of change of $$f(x) = x^3$ from x_1$ = 0 to$$ $$x_2 = 1$?

Accepted Answer

$$1$$

Question 6

Which of the following best describes the graph of $$y = f(x) + c$$ for $$c \u003e 0$$?

Accepted Answer

The graph is shifted $$c$$ units upward.

Question 7

If a function $$f is $$odd, which of the following must be true?

Accepted Answer

$$f(-x) = -f(x)$$ for all $$x$$

Question 8

Given the points $$(13, 57)$$ and $$(18, 76)$$ representing a man's height as a function of age, what is the average rate of change of height between ages 13 and 18?

Accepted Answer

$$\frac{76-57}{18-13} = 3.8$$ inches per year

Question 9

Which of the following equations represents a vertical line?

Accepted Answer

$$x = k$$

Question 10

For the piecewise function $$f(x) = \begin{cases} 3, & x \u003c -1 \ -x^2$, & x \geq -1 \end{cases}$$, what is $$f(-5)$$?

Accepted Answer

$$3$$

Question 11

Which of the following is the correct formula for the slope of the line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 12

Which of the following describes the transformation from $$f(x) to$$ $$g(x) = f(x-3)$$?

Accepted Answer

Shift the graph of $$f(x) 3 $$units to the right.

Question 13

If $$f(x) is a $$function and $$g(x) = 2f(x)$$, what transformation has occurred?

Accepted Answer

The graph of $$f(x) is $$vertically stretched by a factor of 2.

Question 14

Which of the following is the correct difference quotient for $$f(x) = 6x + 1$$?

Accepted Answer

$$\frac{6(x+h) + 1 - (6x + 1)}{h}$$

Question 15

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

Accepted Answer

Reflection about the $$y-$$axis

Question 16

Given $$f(x) = |x|$$, what is the value of $$f(-3)$$?

Accepted Answer

$$3$$

Question 17

Which of the following is the correct formula for the difference quotient of $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$\frac{\frac{1}{x+h} - \frac{1}{x}}{h}$$

Question 18

If two lines are perpendicular, what is true about their slopes $$m_1$$ and $$m_2$$?

Accepted Answer

$$m_1$$ \cdot $$m_2 = -1$

Question 19

Which of the following describes the transformation from $$f(x) to$$ $$g(x) = f(2x)$$?

Accepted Answer

The graph of $$f(x) is $$horizontally shrunk by a factor of 2.

Functions and Their Graphs: Core Concepts and Transformations in Precalculus

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