Question 1

Which of the following describes the domain of the function $$f(x) = \sqrt{x-2} - 4$$?

Accepted Answer

$$x \geq 2$$

Question 2

Given the function $$f(x) = x^3$ - x$$, determine whether it is even, odd, or neither.

Accepted Answer

Odd

Question 3

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

Accepted Answer

$$1$$

Question 4

If a function $$f is $$reflected about the $$x-$$axis, which equation represents the new function?

Accepted Answer

$$y = -f(x)$$

Question 5

A man’s height is measured as a function of his age. At age 13, he was 57 inches tall, and at age 18, he was 76 inches tall. What is the average rate of change of his height between these ages?

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Which transformation occurs when the equation $$y = f(x) + c is $$used?

Accepted Answer

Vertical shift upward by $$c$$ units

Question 8

Given the function $$f(x) = x^2$, what transformations are applied to obtain g(x$$) = $$-(x+2)^2 - 8$?

Accepted Answer

Shift left 2 units, reflect about $$x-$$axis, shift down 8 units

Question 9

Which of the following is the correct formula for the slope of a 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 10

If $$f(x) is $$vertically stretched by a factor of $$c \u003e 1$$, which equation represents the new function?

Accepted Answer

$$y = c f(x)$$

Question 11

Which of the following is true about perpendicular lines in the plane?

Accepted Answer

Their slopes are opposite reciprocals

Question 12

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

Accepted Answer

$$3$$

Question 13

Which of the following is the $$y-$$intercept of the line $$y = 4x - 7$$?

Accepted Answer

$$-7$$

Question 14

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

Accepted Answer

Reflection about the $$y-$$axis

Question 15

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 16

If $$f(x) = |x|$$, which of the following describes the graph of $$g(x) = |3 - x| - 1$$?

Accepted Answer

Shift right 3 units, reflect about $$y-$$axis, shift down 1 unit

Question 17

Which of the following is the equation of a vertical line passing through $$x = 4$$?

Accepted Answer

$$x = 4$$

Question 18

If $$f(x) is $$horizontally shrunk by a factor of $$c \u003e 1$$, which equation represents the new function?

Accepted Answer

$$y = f(cx)$$

Question 19

Which of the following is the $$x-$$intercept of the line $$y = 2x - 6$$?

Accepted Answer

$$3$$

Functions and Graphs: Key Concepts and Transformations in Precalculus

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