Question 1

Which of the following is the correct solution set for the quadratic equation $$x^2 + 5x + 6 = 0$?

Accepted Answer

$$\{-2, -3\}$$

Question 2

Given the function $$f(x) = 4x - 3$$ and $$g(x) = 6x - 6$$, what is $$f(x) - g(x)$$?

Accepted Answer

$$-2x + 3$$

Question 3

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

Accepted Answer

Shift right 2 units, down 3 units

Question 4

What is the domain and range of the function shown in the graph where the domain is all real numbers and the range is $$[0, 8]$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, 8]$$

Question 5

Solve the equation $$3x^2 + 2x - 1 = 0$.

Accepted Answer

Question 6

Which of the following is NOT a function?

Accepted Answer

A relation where an input has two different outputs

Question 7

Given $$f(x) = |x|$$, what is the effect of the transformation $$g(x) = \frac{1}{3}|x-2| + 6$$?

Accepted Answer

Vertical compression by $$\frac{1}{3}$$, right 2 units, up 6 units

Question 8

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

Accepted Answer

$$(x + 1)^2$

Question 9

Which of the following is the solution set for $$2x^2 - 3x - 2 = 0$?

Accepted Answer

$$\left\{2, -\frac{1}{2}\right\}$$

Question 10

Given the graph of $$f(x)$$ with a relative minimum at $$x = 0$$ and $$x = 2$$, what are the relative minimum values?

Accepted Answer

$$-3$$ and $$-1$$

Question 11

Which of the following is the correct solution set for $$x^2 - 6x + 9 = 0$?

Accepted Answer

$$\{3\}$$

Question 12

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

Accepted Answer

$$x^2 + 2x$

Question 13

Which of the following is the solution set for $$x^2 + 2x + 2 = 0$?

Accepted Answer

$$\{-1 + i, -1 - i\}$$

Question 14

Which of the following is the correct solution set for $$x^2 - 4 = 0$?

Accepted Answer

$$\{2, -2\}$$

Question 15

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

Accepted Answer

$$x^2 + x - 1$

Question 16

Which of the following is the solution set for $$x^2 + 3x + 2 = 0$?

Accepted Answer

$$\{-1, -2\}$$

Question 17

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

Accepted Answer

$$(x + 2)^2$

Question 18

Which of the following is the solution set for $$x^2 - 2x - 3 = 0$?

Accepted Answer

$$\{3, -1\}$$

College Algebra Study Guide: Quadratic Equations, Functions, Transformations, and Operations

Study Guide - Practice Questions