Question 1

Solve the equation $$|5x - 2| = 7. $$What are the solutions?

Accepted Answer

$$x = \frac{9}{5},\ x = -1$$

Question 2

Express the solution to $$|3x - 2| + 4 \geq 20 in $$interval notation.

Accepted Answer

$$(-\infty, -\frac{14}{3}] \cup [6, \infty)$$

Question 3

What is the domain of the function $$f(x) = \sqrt{x + 3}$$?

Accepted Answer

$$[-3, \infty)$$

Question 4

Given $$f(x) = \frac{x + 5}{x^2$ + x - 42}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(-\infty, -7) \cup (-7, 6) \cup (6, \infty)$$

Question 5

Which of the following best describes the symmetry of the function $$f(x) = x^3$ - \frac{4}{x}$$?

Accepted Answer

Odd; origin symmetry

Question 6

Find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$f(x) = 2x^2$ - 3x - 4.$$

Accepted Answer

$$4x - 3 + 2h$$

Question 7

Evaluate $$f(x) = 3x^2$ - 2x + 1 at$$ $$x = -2.$$

Accepted Answer

$$17$$

Question 8

Given the graph of $$f(x) in $$image 1, what is the domain of $$f(x)$$?

Accepted Answer

$$[-4, \infty)$$

Question 9

Given the graph of $$f(x) in $$image 2, what is the equation of the function?

Accepted Answer

$$f(x) = \sqrt{x + 4} - 1$$

Question 10

Which transformation is needed to graph $$g(x) = |x - 4| - 2$$ from the basic absolute value function $$f(x) = |x|$$?

Accepted Answer

Shift 4 units right, 2 units down

Question 11

Find the inverse of $$f(x) = x^4$ + 2$$ for $$x \leq 0.$$

Accepted Answer

$$f^{-1}(x$$) = -\sqrt{x - 2}$$

Question 12

Given $$f(x) = 1 + 5x$$ and $$g(x) = \sqrt{x - 1}$$, what is the domain of $$(f + g)(x)$$?

Accepted Answer

$$[1, \infty)$$

Question 13

Which of the following is the correct point-slope form for the line with slope 3 passing through $$(-7, 2)$$?

Accepted Answer

$$y - 2 = 3(x + 7)$$

Question 14

Given $$f(x) = 3x + 1$$ and $$g(x) = 2x - x^2$, what is the domain of $$\left(\frac{f}{g}\right)(x)$$?

Accepted Answer

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

Question 15

Which of the following best describes the range of the function graphed in image 1?

Accepted Answer

$$[-1, \infty)$$

Question 16

Given $$f(x) = 1 + 5x$$ and $$g(x) = \sqrt{x - 1}$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$1 + 5\sqrt{x - 1}$$

Question 17

Which of the following is the correct inverse of $$f(x) = \frac{2x + 1}{x}$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{1}{x - 2}$$

Question 18

Which of the following describes the transformation for $$f(x) = -(x - 4)^2$ + 1$$ from the basic quadratic function $$y = x^2$?

Accepted Answer

Shift 4 units right, reflect over x-axis, shift 1 unit up

Question 19

Given $$f(x) = x^2$ + 3x$$, find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$2x + 3 + h$$

College Algebra Module 2 Exam Study Guide – Step-by-Step Guidance

Study Guide - Practice Questions