Q: Which of the following best illustrates an application of a logarithmic function in a real-world scenario, as expected in MATH 103?

Modeling the pH level of a solution, where $$\text{pH} = -\log_{10}[H^+]$$

Q: Which of the following is a correct example of a piecewise-defined function, as studied in MATH 103?

$$f(x) = \begin{cases} x^2$ & x \u003c 0 \\ 2x + 1 & x \geq 0 \end{cases}$$

Question 1

Which of the following best describes the main focus of MATH 103 as outlined in the syllabus?

Accepted Answer

Analyzing and interpreting the behavior and nature of functions, and solving real-world application problems using algebraic functions.

Question 2

A student is modeling the population growth of a bacteria culture using an exponential function. Which type of function should they use according to the course competencies?

Accepted Answer

An exponential function: $$y = ab^x$$

Question 3

Which of the following is NOT a required material or resource for MATH 103?

Accepted Answer

A physical textbook purchased from the bookstore

Question 4

A student is solving the equation $$2x^2 - 8 = 0$ as part of a written assignment. According to course expectations, what should the student do to receive full credit?

Accepted Answer

Show all steps, explain their reasoning, and use correct mathematical notation.

Question 5

Which of the following best illustrates an application of a logarithmic function in a real-world scenario, as expected in MATH 103?

Accepted Answer

Modeling the pH level of a solution, where $$	ext{pH} = -\log_{10}[H^+]$$

Question 6

A student is asked to solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 4 \end{cases}. $$Which process aligns with the course's Student Learning Outcomes?

Accepted Answer

Applying algebraic methods such as substitution or elimination to find the solution.

Question 7

Which of the following is a correct example of a piecewise-defined function, as studied in MATH 103?

Accepted Answer

$$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x + 1 & x \geq 0 \end{cases}$$

Question 8

A student is asked to graph the function $$f(x) = |x - 3|. $$According to the course requirements, which of the following is the best practice?

Accepted Answer

Draw the graph by hand, label all axes and points, and choose an appropriate scale.

Question 9

Which of the following is a real-world application of a rational function, as expected in MATH 103?

Accepted Answer

Calculating the average cost per item, $$C(x) = \frac{500 + 20x}{x}$$, where $$x is $$the number of items produced.

Question 10

A student is given the exponential equation $$5e^{2x} = 20$. What is the correct first step to solve for x$?

Accepted Answer

Divide both sides by $$5 to $$isolate the exponential term.

Question 11

Which of the following best describes the grading policy for MATH 103?

Accepted Answer

Grades are based on points earned from homework, quizzes, written assignments, discussions, tests, and the final exam.

Question 12

A student is asked to solve the inequality $$x^2 - 4x + 3$$ \u003c 0$$. Which of the following is the correct solution?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 13

Which of the following is an example of a function that is NOT one-to-one?

Accepted Answer

$$f(x) = x^2$

Question 14

A student is modeling the depreciation of a car's value using the function $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years. What type of function is this?

Accepted Answer

An exponential decay function

Question 15

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

Accepted Answer

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

Question 16

A student is asked to solve $$\log_2$(x) = 5. $$What is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 17

Which of the following best describes the policy on late assignments for MATH 103?

Accepted Answer

Homework may be submitted late until the final submission date, but quizzes, written assignments, and discussions have strict deadlines.

Question 18

A student is asked to model the cooling of a cup of coffee using Newton's Law of Cooling, which is an exponential function. Which equation best represents this scenario?

Accepted Answer

$$T(t) = T_{	ext{env}} + (T_0$ - T_{	ext{env}})e$$^{-kt}$$

Question 19

Which of the following is a correct application of the absolute value function in a real-world context?

Accepted Answer

Calculating the distance between two points on a number line: $$|x_1$ - x_2$|$$

Question 20

A student is asked to solve the radical equation $$\sqrt{x + 5} = x - 1. $$Which of the following is the correct first step?

Accepted Answer

Square both sides to eliminate the square root.

MATH 103 College Algebra: Syllabus and Course Structure Study Guide

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