Question 1

Which of the following relations is NOT a function?

Accepted Answer

A relation where an input is paired with two different outputs.

Question 2

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

Accepted Answer

$$25$$

Question 3

If $$g(x) = x^2$ and h(x) = 3x + 2$, what is (g + h)(x$$)$$?

Accepted Answer

$$x^2 + 3x + 2$

Question 4

Find the composition $$(f \circ g)(x) if$$ $$f(x) = x + 1$$ and $$g(x) = 2x.$$

Accepted Answer

$$2x + 1$$

Question 5

What is the difference quotient for $$f(x) = x^2$?

Accepted Answer

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

Question 6

Which of the following is the inverse of $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 5}{3}$$

Question 7

Solve the quadratic equation $$x^2 - 4x + 4 = 0$.

Accepted Answer

$$x = 2$$

Question 8

Which of the following is a characteristic of a quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

The graph is a parabola.

Question 9

If $$f(x) = x^3$ - 2x^2$ + x - 2$$, which theorem can be used to find its zeros?

Accepted Answer

Fundamental Theorem of Algebra

Question 10

Divide $$x^3$$ + $$2x^2 - x + 4$ by x - 1$ using synthetic division. What is the remainder?

Accepted Answer

$$5$$

Question 11

Which of the following is the correct form of the exponential function?

Accepted Answer

$$f(x) = a \cdot b^x$$

Question 12

Rewrite $$y = 2^x in $$logarithmic form.

Accepted Answer

$$x = \log_2$ y$$

Question 13

Expand $$\log_2$(8x)$$ using properties of logarithms.

Accepted Answer

$$\log_2$ 8 + \log_2$ x$$

Question 14

Solve the exponential equation $$3^x = 81.$$

Accepted Answer

$$x = 4$$

Question 15

A population of bacteria grows according to $$P(t) = 500e$$^{0.03t}$$. What is the population after 10 hours?

Accepted Answer

$$P(10) = 500e$$^{0.3}$$

Question 16

Solve the system of equations: $$x + y + z = 6$$, $$2x - y + z = 3$$, $$x - 2y + 3z = 14.$$

Accepted Answer

$$x = 2, y = 1, z = 3$$

Question 17

Which of the following is a solution to the nonlinear system $$x^2$$ + $$y^2 = 25$, y = x + 1$?

Accepted Answer

$$(3, 4)$$

Question 18

Which of the following best describes the graph of a rational function?

Accepted Answer

It may have vertical and horizontal asymptotes.

Question 19

If $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

All real numbers except $$x = 2$$

MTH 112 Precalculus Algebra Syllabus and Course Overview

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