Question 1

Which of the following equations represents the English sentence: "The y-value is the difference between six and three times the x-value"?

Accepted Answer

$$y = 6 - 3x$$

Question 2

A motorcycle repair shop charged a customer $$404, listing 74 $$for parts and the remainder for labor. If the cost of labor is $27.50 per hour, how many hours of labor did it take to repair the motorcycle?

Accepted Answer

$$12$$

Question 3

Solve the equation $$\dfrac{1}{2}x - \dfrac{1}{3}x = 1 - \dfrac{3}{4}x. $$What is the solution?

Accepted Answer

$$x = -11$$

Question 4

Which of the following is the standard form of the equation of a circle with center $$(-8, 5)$$ and radius $$11$$?

Accepted Answer

$$(x + 8)^2$ + (y - 5)^2$ = 121$$

Question 5

Given $$f(x) = 2x^2$ - 5x + 2$$, what is $$f(x+2)$$?

Accepted Answer

$$2(x+2)^2 - 5(x+2) + 2$

Question 6

Which of the following best describes the solution set to the inequality $$3x - 4 \leq 8 in $$interval notation?

Accepted Answer

$$(-\infty, 4]$$

Question 7

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

Accepted Answer

$$f(g(2)) = f(3) = 9 - 9 + 4 = 4$$

Question 8

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 1 = 0$ using the quadratic formula?

Accepted Answer

$$x = 3 \pm 2\sqrt{2}$$

Question 9

Which of the following statements is true about the function $$f(x) = x^3$ - 5x$$?

Accepted Answer

The function is odd.

Question 10

What is the average rate of change of $$f(x) = 4x^2$ - x + 2$$ from $$x = 1 to$$ $$x = 6$$?

Accepted Answer

$$7$$

Question 11

Given the function $$f(x) = \dfrac{1}{x-3}$$, what is the domain of $$f$$?

Accepted Answer

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

Question 12

Which of the following is the correct equation of the line passing through $$(-3, 1)$$ and parallel to $$y = -\dfrac{1}{2}x - 5$$?

Accepted Answer

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

Question 13

If $$f(x) = 2x^2$ - 3x + 1$$, what is the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$4x + 2h - 3$$

Question 14

Which of the following is the inverse of the function $$f(x) = 4x - 2$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x+2}{4}$$

Question 15

Solve the absolute value equation $$|2x - 5| = 9.$$

Accepted Answer

$$x = 7, x = -2$$

Question 16

A farmer purchased 730 feet of fencing to enclose a rectangular garden. If the length of the garden is 5 feet more than 3 times the width, what are the dimensions of the garden?

Accepted Answer

Length: 275 ft, Width: 90 ft

Question 17

Which of the following is the correct solution to the radical equation $$\sqrt{2x - 5} = 1$$?

Accepted Answer

$$x = 3$$

Question 18

Given the function $$f(x) = x^2$ - 4x + 3$$, for which value(s) of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1, x = 3$$

Question 19

Which of the following describes the transformation from $$f(x) = x^2$ to g(x$$) = $$2(x-3)^2 + 1$?

Accepted Answer

Shift right 3 units, stretch vertically by 2, shift up 1 unit

Question 20

What is the distance between the points $$(2, 7)$$ and $$(7, -3)$$?

Accepted Answer

$$\sqrt{66}$$

College Algebra Study Guide: Test 1 - Modules 1 - 3

Study Guide - Practice Questions

Study Guide - Flashcards