Question 1

Convert the decimal $$0.34 to $$percent notation.

Accepted Answer

$$34\%$$

Question 2

Which of the following is the correct percent notation for the fraction $$\dfrac{3}{8}$$?

Accepted Answer

$$37.5\%$$

Question 3

Calculate $$\dfrac{3}{4} - \dfrac{5}{8} as a $$single fraction in simplest form.

Accepted Answer

$$\dfrac{1}{8}$$

Question 4

Solve the equation $$2x - 2 = 3x + 3.$$

Accepted Answer

$$x = -5$$

Question 5

Find the equation of the circle with center $$(-2, 3)$$ and passing through the point $$(1, 7).$$

Accepted Answer

$$(x + 2)^2$ + (y - 3)^2$ = 25$$

Question 6

Which of the following relations is NOT a function?

Accepted Answer

A relation where the graph fails the vertical line test.

Question 7

Given the function $$f(x) = 2x + 1$$, what is the slope of the graph of $$f$$ and what does it represent?

Accepted Answer

Slope is $$2$$, representing the rate of change of $$f$$ with respect to $$x.$$

Question 8

Suppose a $$20-lb $$weight stretches a spring $$10$$ inches. Using Hooke's Law $$F = kx$$, what is the spring constant $$k$$?

Accepted Answer

$$k = 2 lb/in$

Question 9

If the spring constant $$k is$$ $$2 lb/in$$, how far will a $$25-lb $$weight stretch the spring?

Accepted Answer

$$12.5$$ inches

Question 10

Find the $$x- $$and $$y-$$intercepts for the line $$2x + 3y = 6.$$

Accepted Answer

$$x-$$intercept: $$(3, 0)$$; $$y-$$intercept: $$(0, 2)$$

Question 11

Given the points $$A(2, 5)$$ and $$B(8, 11)$$, what is the distance between them?

Accepted Answer

$$6\sqrt{2}$$

Question 12

What is the midpoint of the segment joining $$(2, 5)$$ and $$(8, 11)$$?

Accepted Answer

$$(5, 8)$$

Question 13

Which of the following equations represents a line perpendicular to $$y = 2x + 1$$?

Accepted Answer

$$y = -\dfrac{1}{2}x + 3$$

Question 14

Solve the inequality $$-5 \leq -2(x + 4) - 5 \u003c 5$$ and write the solution in interval notation.

Accepted Answer

$$(-7, 2]$$

Question 15

Given $$f(x) = x + 3$$ for $$-3 \leq x \u003c 1$$ and $$f(x) = 2x - 1$$ for $$1 \leq x \leq 3$$, what is $$f(2)$$?

Accepted Answer

$$5$$

Question 16

A biologist models the population of a bacteria culture with $$P(t) = 500 + 20t$$, where $$t is $$time in hours. What does the $$20$$ represent?

Accepted Answer

The rate of change of the population per hour

Question 17

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

Accepted Answer

$$x \geq 2$$

Question 18

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

Accepted Answer

$$8$$

Question 19

A car rental company charges a flat fee of $$\50$ plus $$\$$0.20$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 0.20m + 50$$

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

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