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

$$f(g(2)) = 2 \times 4 + 3 = 11$$

Q: A medical researcher uses the exponential function $$P(t) = P_0$ e$$^{rt}$$ to model bacterial growth. If P_0$ = 100$$, $$r = 0.05$$, and $$t = 10$$, what is the population after 10 hours?

$$P(10) = 100 \times e$$^{0.5}$$ \approx 164.87$$

Question 1

Which of the following best describes the primary focus of Math 105 – Intermediate Algebra at UAA?

Accepted Answer

Equations and applications involving linear, quadratic, rational, and radical functions, as well as introduction to exponential and logarithmic functions.

Question 2

A student needs to solve the following quadratic equation for $$x$$: $$x^2 - 5x + 6 = 0$. Which method is most appropriate for this type of equation?

Accepted Answer

Factoring the quadratic.

Question 3

If $$f(x) = 2x + 3$$ and $$g(x) = x^2$, what is the value of (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 2 	imes 4 + 3 = 11$$

Question 4

Which of the following is the correct inverse function of $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 5

A medical researcher uses the exponential function $$P(t) = P_0$ e$$^{rt}$$ to model bacterial growth. If P_0$ = 100$$, $$r = 0.05$$, and $$t = 10$$, what is the population after 10 hours?

Accepted Answer

$$P(10) = 100 	imes e$$^{0.5}$$ \approx 164.87$$

Question 6

Which of the following best represents the graph of a quadratic function?

Accepted Answer

A parabola.

Question 7

A student is asked to solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 4 \end{cases}. $$What is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 8

Which of the following is a real-world application of rational functions?

Accepted Answer

Determining the concentration of a drug in the bloodstream over time.

Question 9

If $$f(x) = \sqrt{x}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 0$$

Question 10

A student is given the logarithmic equation $$\log_{2}(x) = 5. $$What is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 11

Which of the following statements about academic integrity in Math 105 is correct?

Accepted Answer

Students must work individually on quizzes and tests.

Question 12

If $$f(x) = |x - 3|$$, what is the value of $$f(-2)$$?

Accepted Answer

$$f(-2) = |-2 - 3| = |-5| = 5$$

Question 13

Which of the following is NOT a prerequisite for Math 105?

Accepted Answer

Completion of Calculus I.

Question 14

A student is asked to graph $$y = 2x + 1. $$What is the slope of the line?

Accepted Answer

$$2$$

Question 15

Which of the following is the correct solution to the radical equation $$\sqrt{x + 4} = 6$$?

Accepted Answer

$$x = 32$$

Question 16

A student is given the rational function $$f(x) = \frac{1}{x - 2}. $$What is the vertical asymptote?

Accepted Answer

$$x = 2$$

Question 17

Which of the following best describes the grading policy for Math 105?

Accepted Answer

Homework and reviews are graded automatically; quizzes and tests are graded by the professor.

Question 18

If a student misses the deadline to sign up for MyLabMath, what may happen according to the syllabus?

Accepted Answer

The student may be dropped from the class roster at the professor's discretion.

Question 19

Which of the following is a core competency for students completing Math 105?

Accepted Answer

Demonstrate graphical competency for linear, quadratic, absolute value, rational, and square root functions.

Math 105 – Intermediate Algebra Syllabus and Course Overview

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