Question 1

Which of the following graphs does NOT represent a function?

Accepted Answer

A graph where a vertical line crosses the curve at two points.

Question 2

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

Accepted Answer

Odd

Question 3

Which transformation results in the graph of $$f(x)$$ being reflected across the y-axis?

Accepted Answer

$$f(-x)$$

Question 4

If $$f(x) = |x|$$, what is the vertex of the graph of $$f(x - 3) + 2$$?

Accepted Answer

$$(3, 2)$$

Question 5

Which of the following describes a vertical stretch of the function $$f(x) by a $$factor of 4?

Accepted Answer

$$4f(x)$$

Question 6

Given the quadratic function $$f(x) = 2x^2$ - 8x + 6$$, what are the coordinates of its vertex?

Accepted Answer

$$(2, -2)$$

Question 7

A cost function for producing $$x$$ bicycles is $$C(x) = 50x + 200. If $$each bicycle sells for $$C(x)/x$$, what is the average cost per bicycle when $$x = 10$$?

Accepted Answer

$$70$$

Question 8

Which of the following intervals is $$f(x) = x^2$ decreasing?

Accepted Answer

$$(-\infty, 0)$$

Question 9

If a population grows from $$0.32$$ grams at $$t = 3$$ hours to $$0.51$$ grams at $$t = 5$$ hours, what is the average rate of growth?

Accepted Answer

$$0.093$$ grams/hour

Question 10

Which of the following is the correct formula for the average rate of change of a function $$f(x)$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 11

Given the piecewise function $$f(x) = \begin{cases} x^2$, & x \u003c 0 \ 2x + 1, & x \geq 0 \end{cases}$$, what is the value of $$f(0)$$?

Accepted Answer

$$1$$

Question 12

Which of the following statements about symmetry is TRUE?

Accepted Answer

A function is even if it is symmetric about the y-axis.

Question 13

For the function $$f(x) = (x + 3)^2$ + 2$$, what is the vertex?

Accepted Answer

$$(-3, 2)$$

Question 14

If $$f(x) = x^2$ - 4$$, what are the x-intercepts?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 15

Which of the following best describes the secant line between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$) on a $$curve?

Accepted Answer

A line passing through both $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$

Question 16

If $$f(x) = x^2$ - 4$$, what is the y-intercept?

Accepted Answer

$$(0, -4)$$

Question 17

Which of the following is the correct step for completing the square for $$f(x) = x^2$ + 6x + 5$$?

Accepted Answer

Add $$\left(\frac{6}{2}\$$right)^2$$ to both sides

Question 18

A function $$f(x) is $$defined as even. Which of the following must be true for all $$x in $$the domain?

Accepted Answer

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

Question 19

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$f(g(1))$$?

Accepted Answer

$$1$$

Question 20

Which of the following best describes the interval where $$f(x) = -x^2$ is increasing?

Accepted Answer

$$(-\infty, 0)$$

Algebra & Precalculus: Functions, Graphs, and Applications Study Guide

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