Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x + 3$$, what is the equation of the line perpendicular to $$f(x)$$ that passes through the point $$(1, 5)$$?

Accepted Answer

$$y = -\frac{1}{2}x + \frac{11}{2}$$

Question 3

A chemist is tracking the temperature of a reaction over time. The temperature $$T (in $$degrees Celsius) is modeled by $$T(t) = -4t^2$ + 16t + 20$$, where $$t is $$time in hours. What is the maximum temperature reached during the reaction?

Accepted Answer

$$52$$ degrees Celsius

Question 4

Which of the following is the correct solution set for the inequality $$2x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 6$$

Question 5

A company models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -0.5x^2$ + 10x - 12. $$For what number of units sold does the company break even (i.e., $$P(x) = 0$$)?

Accepted Answer

$$x = 12 or$$ $$x = 2$$

Question 6

Which of the following is the graph of a piecewise-defined function?

Accepted Answer

A graph that consists of two or more distinct parts, each defined by a different rule over different intervals.

Question 7

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

Accepted Answer

$$9$$

Question 8

A medical researcher models the concentration $$C of a $$drug in the bloodstream by $$C(t) = 5e$$^{-0.3t}$$, where t$ is time in hours. What is the concentration after 2 hours, rounded to two decimal places?

Accepted Answer

$$2.74$$

Question 9

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

Accepted Answer

Shift right 3 units and up 2 units.

Question 10

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 3$$

Question 11

A biologist is studying the growth of a bacteria population, which can be modeled by $$P(t) = 100 \cdot 2^t$$, where $$t is $$time in hours. How many bacteria will there be after 3 hours?

Accepted Answer

$$800$$

Question 12

Which of the following is the correct equation of a line passing through the points $$(2, 5)$$ and $$(4, 9)$$?

Accepted Answer

$$y = 2x + 1$$

Question 13

If $$f(x) = |x - 2|$$, what is the value of $$f(-1)$$?

Accepted Answer

$$3$$

Question 14

A real estate agent uses the linear model $$y = 250x + 50,000 to $$estimate the price $$y (in $$dollars) of a house with $$x$$ square feet. What is the estimated price of a house with $$1,800$$ square feet?

Accepted Answer

$$500,000$$

Question 15

Which of the following is the solution to the quadratic equation $$x^2 - 6x + 5 = 0$?

Accepted Answer

$$x = 1 or$$ $$x = 5$$

Question 16

Which of the following best describes the symmetry of the graph of $$y = x^2$?

Accepted Answer

It is symmetric about the $$y-$$axis.

Question 17

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

Accepted Answer

$$8$$

Question 18

A student is analyzing the cost of a cell phone plan, which charges a base fee of $$\20$ plus $$\$$0.10$$ per minute. Which function models the total cost $$C$$ for $$m$$ minutes?

Accepted Answer

$$C(m) = 0.10m + 20$$

Question 19

Which of the following is the correct solution to the inequality $$|x - 4| \leq 3$$?

Accepted Answer

$$1 \leq x \leq 7$$

Question 20

If the function $$f(x) is $$defined as $$f(x) = \begin{cases} x + 2 & 	ext{if } x \u003c 0 \ 2x - 1 & 	ext{if } x \geq 0 \end{cases}$$, what is $$f(-3) + f(2)$$?

Accepted Answer

$$2$$

College Algebra: Course Schedule and Topic Overview

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