Question 1

Solve the inequality $$2x - 5 \leq 7$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 6]$$

Question 2

Which of the following graphs represents the solution set to $$x \u003e -2$$?

Accepted Answer

A number line with an open circle at $$-2$$ and shading to the right

Question 3

Solve the compound inequality $$-1 \u003c 2x + 3 \leq 7$$ and express the solution in interval notation.

Accepted Answer

$$(-2, 2]$$

Question 4

Given the function $$f(x) = x^2$ - 4x + 3$$, what is the value of $$f(2)$$?

Accepted Answer

$$-1$$

Question 5

Which of the following equations defines $$y as a $$function of $$x$$?

Accepted Answer

$$y = \sqrt{x}$$

Question 6

Use the vertical line test to determine if the graph of a circle centered at the origin is a function of $$x. $$Which statement is correct?

Accepted Answer

It is not a function of $$x$$

Question 7

Find the slope of the line passing through the points $$(2, 3)$$ and $$(5, 11).$$

Accepted Answer

Question 8

Given the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ 2x-1 & x \geq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-1$$

Question 9

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

Accepted Answer

Odd

Question 10

A function $$f is $$increasing on the interval $$(-\infty, 2)$$ and decreasing on $$(2, \infty). $$What is the nature of $$x=2$$?

Accepted Answer

Relative maximum

Question 11

Solve the inequality $$|2x - 3| \u003c 5$$ and express the solution in interval notation.

Accepted Answer

$$(-1, 4)$$

Question 12

Which of the following best describes the symmetry of the graph of $$f(x) = x^4$?

Accepted Answer

Symmetric with respect to the $$y-$$axis

Question 13

Given the function $$f(x) = 2x^2$ - 8x + 6$$, find the vertex of the parabola.

Accepted Answer

$$(2, -2)$$

Question 14

Find the $$y-$$intercept of the line with equation $$3x - 2y = 6.$$

Accepted Answer

$$(0, -3)$$

Question 15

A company charges $$f(w) = 0.5w + 0.25$$ dollars to mail a letter weighing $$w$$ ounces. What is the cost to mail a letter that weighs $$3$$ ounces?

Accepted Answer

$$1.25$$

Question 16

Which of the following intervals describes where the function $$f(x) is $$constant if $$f(x) is a $$horizontal line?

Accepted Answer

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

Question 17

Given the equation $$y = -2x + 5$$, what is the slope and $$y-$$intercept?

Accepted Answer

Slope: $$-2$$, $$y-$$intercept: $$5$$

Question 18

If $$f(x) = x^2$ - 4$$ and $$g(x) = 2x + 1$$, what is $$(f + g)(3)$$?

Accepted Answer

$$10$$

Question 19

Which of the following is the equation of the line passing through $$(0, 2)$$ with slope $$-3$$?

Accepted Answer

$$y = -3x + 2$$

Question 20

Determine the domain of the function $$f(x) = \sqrt{x - 1}.$$

Accepted Answer

$$[1, \infty)$$

College Algebra Study Guide: Equations, Inequalities, Functions, and Graphs

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