Question 1

Which of the following best describes the primary focus of Precalculus 1 at CSN, as outlined in the course description?

Accepted Answer

An in-depth investigation of algebraic functions and their graphs, and solutions of systems of equations.

Question 2

A student is solving the equation $$2^x = 16. $$Which property of exponents should they use to solve for $$x$$?

Accepted Answer

The definition of exponential equations: $$a^x = b \implies x = \log_a b$$

Question 3

Which of the following is the correct solution to the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 3, y = 2$$

Question 4

A biologist models population growth with the function $$P(t) = 1000e$$^{0.05t}$$. What type of function is this, and what does the parameter 0.05$ represent?

Accepted Answer

It is an exponential function; $$0.05 is $$the growth rate.

Question 5

Given the function $$f(x) = x^2$ - 4x + 7$$, what is the vertex of its graph?

Accepted Answer

The vertex is at $$(2, 3).$$

Question 6

A medical researcher uses the logarithmic function $$C(t) = \log_{10}(t+1) to $$model the concentration of a drug in the bloodstream over time. If $$t = 9$$, what is $$C(9)$$?

Accepted Answer

$$C(9) = \log_{10}(10) = 1$$

Question 7

Which of the following statements about function notation is correct?

Accepted Answer

If $$f(x) = 2x + 3$$, then $$f(4) = 11.$$

Question 8

A chemical reaction is modeled by $$y = 5e$$^{-0.2x}$$. What happens to y$ as x$ increases?

Accepted Answer

$$y$$ decreases and approaches zero.

Question 9

Which of the following is the correct graph for the function $$f(x) = |x - 3|$$?

Accepted Answer

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

Question 10

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

Accepted Answer

$$x = 32$$

Question 11

Which of the following is NOT a property of functions?

Accepted Answer

A function can assign multiple outputs to a single input.

Question 12

A real-world scenario: The cost $$C to $$produce $$x$$ units of a product is modeled by $$C(x) = 50x + 200. $$What does the $$200$$ represent?

Accepted Answer

The fixed cost, independent of the number of units produced.

Question 13

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

Accepted Answer

$$(f \circ g)(2) = f(g(2)) = f(3) = 9$$

Question 14

A student is given the quadratic equation $$x^2 - 6x + 8 = 0$. What are the solutions?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 15

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

Accepted Answer

A parabola opening downward.

Question 16

A student is asked to solve the system: $$\begin{cases} 2x + 3y = 12 \ x - y = 1 \end{cases}. $$What is the solution?

Accepted Answer

$$x = 3, y = 1$$

Question 17

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 18

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

Accepted Answer

All real numbers except $$x = 2$$

Question 19

A business models its revenue with $$R(x) = 100x - x^2$, where x$ is the number of units sold. What number of units maximizes revenue?

Accepted Answer

$$x = 50$$

Question 20

Which of the following is the solution to the exponential equation $$3^{x} = 81$?

Accepted Answer

$$x = 4$$

Precalculus I (Math 126E) Syllabus and Course Structure – Summer 2026

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