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

$$f(g(2)) = 2 \times 1 + 1 = 3$$

Question 1

Which of the following best describes the primary focus of Pre-Calculus Algebra as outlined in the syllabus?

Accepted Answer

To develop skills in solving equations, inequalities, and modeling functions with and without technology.

Question 2

A student is asked to solve the equation $$|2x - 5| = 9. $$Which of the following is the correct set of solutions?

Accepted Answer

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

Question 3

Which of the following is NOT a recommended tool or material for this Pre-Calculus Algebra course?

Accepted Answer

Scientific calculator without graphing capabilities

Question 4

Given the quadratic function $$f(x) = -2x^2$ + 8x - 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 5)$$

Question 5

A real-world scenario: A company models its profit $$P (in $$thousands of dollars) as $$P(x) = -3x^2$ + 18x - 12$$, where $$x is $$the number of units sold (in hundreds). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$24$$ thousand dollars at $$x = 3$$ hundred units.

Question 6

Which of the following statements about academic honesty in this course is TRUE?

Accepted Answer

Using unauthorized resources on tests is considered academic dishonesty.

Question 7

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

Accepted Answer

$$f(g(2)) = 2 	imes 1 + 1 = 3$$

Question 8

Which of the following best describes the solution set for the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 9

A student is using the distance formula to find the distance between the points $$(2, -1)$$ and $$(5, 3). $$Which of the following is the correct answer?

Accepted Answer

$$5$$

Question 10

Which of the following is a correct application of the Fundamental Theorem of Algebra?

Accepted Answer

A polynomial of degree $$n$$ has exactly $$n$$ complex roots, counting multiplicities.

Question 11

Given the exponential function $$f(x) = 3 \cdot 2^x$$, what is $$f(4)$$?

Accepted Answer

$$48$$

Question 12

Which of the following best describes the graph of $$y = \log_2$(x)$$?

Accepted Answer

It passes through $$(1, 0)$$ and increases slowly for large $$x.$$

Question 13

A system of equations is given by $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1)$$

Question 14

Which of the following is the correct inverse of the function $$f(x) = 5x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 7}{5}$$

Question 15

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How much remains after 10$ years?

Accepted Answer

$$60.65$$

Question 16

Which of the following is a correct interpretation of the solution to the equation $$\log_{10}(x) = 2$$?

Accepted Answer

$$x = 100$$

Question 17

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

Accepted Answer

$$21$$

Question 18

Which of the following is the correct solution to the rational equation $$\frac{2}{x} = 4$$?

Accepted Answer

$$x = 0.5$$

Question 19

A student is asked to solve the system using matrices: $$\begin{cases} x + 2y = 5 \ 3x - y = 4 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1.5)$$

Question 20

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

Accepted Answer

$$x \geq 2$$

Pre-Calculus Algebra (MAT-171) Syllabus and Course Structure Overview

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