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

$$f(g(2)) = 3 \times 4 - 2 = 10$$

Question 1

Which of the following best describes the main purpose of College Algebra as outlined in the syllabus?

Accepted Answer

To develop problem-solving skills and apply algebraic concepts to real-world scenarios.

Question 2

A student is solving the equation $$2x^2 - 5x + 3 = 0$. Which method would be most appropriate to find the solutions?

Accepted Answer

Factoring the quadratic equation.

Question 3

Which of the following is a key requirement for passing Math 1220 according to the syllabus?

Accepted Answer

Receiving a final grade of 73% or higher.

Question 4

Given the exponential equation $$5^{x} = 125$, what is the value of x$?

Accepted Answer

$$x = 3$$

Question 5

Which of the following best demonstrates the correct use of function notation?

Accepted Answer

$$f(x) = 2x + 1$$

Question 6

A biologist models the population of a bacteria culture with the function $$P(t) = 200e$$^{0.3t}$$, where t$ is in hours. What is the population after 5 hours?

Accepted Answer

$$P(5) = 200e$$^{1.5}$$

Question 7

Which of the following is NOT a property of logarithms?

Accepted Answer

$$\log_b(x + y) = \log_b(x) \cdot \log_b(y)$$

Question 8

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 9

Which of the following best describes the graph of $$y = |x - 3|$$?

Accepted Answer

A V-shaped graph with vertex at $$(3, 0)$$

Question 10

A student is asked to solve the rational equation $$\frac{2}{x} + 3 = 5. $$What is the correct solution?

Accepted Answer

$$x = 2$$

Question 11

Which of the following is the correct way to express the solution set for the inequality $$x^2 - 4$$ \u003c 0$$?

Accepted Answer

$$(-2, 2)$$

Question 12

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

Accepted Answer

$$f(g(2)) = 3 	imes 4 - 2 = 10$$

Question 13

A medical researcher uses the function $$C(t) = 100e$$^{-0.05t}$$ to model the concentration of a drug in the bloodstream over time t$ (in hours). What is the initial concentration?

Accepted Answer

$$C(0) = 100$$

Question 14

Which of the following is a correct application of the quadratic formula to solve $$x^2 - 6x + 8 = 0$?

Accepted Answer

$$x = \frac{6 \pm \sqrt{(-6)^2$ - 4 \cdot 1 \cdot 8}}{2}$$

Question 15

A student is analyzing the function $$f(x) = \frac{1}{x-2}. $$What is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 2$$

Question 16

Which of the following is an example of a real-world application of a system of linear equations?

Accepted Answer

Determining the intersection point of two supply and demand curves in economics.

Question 17

If $$\log_2$(x) = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 18

Which of the following best describes the transformation of the graph $$y = x^2$ to y = (x$$ - $$4)^2 + 3$?

Accepted Answer

Shift right 4 units and up 3 units.

College Algebra Syllabus and Course Structure Study Guide

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