Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{(0,1),\ (1,2),\ (2,3),\ (0,4)\}$$

Question 2

Evaluate $$f(3)$$ for $$f(x) = \dfrac{x^2$ + 6}{x^3$ + 6x}.$$

Accepted Answer

$$\dfrac{15}{33}$$

Question 3

A graph fails the vertical line test if:

Accepted Answer

Some vertical line crosses the graph at more than one point.

Question 4

Given the function $$f(x) = x^3$ - 3x^2$ + 1$$, which of the following is a relative minimum?

Accepted Answer

At $$x = 2$$, $$f(2) = -3$$

Question 5

For the piecewise function $$f(x) = \begin{cases} x-2 & 	ext{if } x \u003e -5 \ -(x-2) & 	ext{if } x \leq -5 \end{cases}$$, what is $$f(-8)$$?

Accepted Answer

$$6$$

Question 6

Find and simplify the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$ for $$f(x) = 9x^2$, h$$ 
eq 0$$.

Accepted Answer

$$18x + 9h$$

Question 7

Which of the following best describes the domain of $$f(x) = \dfrac{1}{x^2$ + 2x - 3}$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, 1) \cup (1, \infty)$$

Question 8

What is the slope and y-intercept of the line $$5x + y - 6 = 0$$?

Accepted Answer

Slope: $$-5$$, y-intercept: $$6$$

Question 9

Write the equation of the line passing through $$(4,2)$$ and perpendicular to $$y = 9x + 7 in $$point-slope form.

Accepted Answer

$$y - 2 = -\dfrac{1}{9}(x - 4)$$

Question 10

Find the average rate of change of $$f(x) = 2x$$ from $$x_1 = 2$ to x_2$ = 8.$$

Accepted Answer

$$2$$

Question 11

Which interval describes where the function $$f(x) = x^3$ - 3x^2$ + 1 is $$increasing?

Accepted Answer

$$(-\infty, 0) \cup (2, \infty)$$

Question 12

Given the equation $$y = -\dfrac{2}{5}x + 3$$, what is the slope and y-intercept?

Accepted Answer

Slope: $$-\dfrac{2}{5}$$, y-intercept: $$3$$

Question 13

Solve for $$x in $$the equation $$3x - 2 = -17.$$

Accepted Answer

$$x = -5$$

Question 14

Write the equation of the line passing through $$(2,3)$$ and parallel to $$4x + y - 5 = 0 in $$slope-intercept form.

Accepted Answer

$$y = -4x + 11$$

Question 15

A chemical reaction's rate is modeled by $$f(x) = x^2$ + 2x - 3. $$For which $$x-$$values is the reaction rate undefined?

Accepted Answer

The reaction rate is defined for all real $$x$$

Question 16

If a function's graph passes the vertical line test, which of the following must be true?

Accepted Answer

Each $$x-$$value in the domain corresponds to exactly one $$y-$$value.

Question 17

Given $$f(x) = x^2$ + 2x - 3$$, what is $$f(-1)$$?

Accepted Answer

$$-4$$

Question 18

A medical dosage is modeled by $$f(x) = 9x^2$. If the dosage increases from x = 1$ to x = 3$, what is the average rate of change?

Accepted Answer

$$36$$

Question 19

Which of the following best describes the range of $$f(x) = x^2$ + 6$$?

Accepted Answer

$$[6, \infty)$$

Question 20

A population model is given by $$f(x) = x^2$ + 6x. $$What is the value of $$f(-3)$$?

Accepted Answer

$$-9$$

College Algebra Worksheet Guidance: Functions, Graphs, and Linear Equations

Study Guide - Practice Questions