Question 1

Which of the following best describes the solution set of the equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 2

A company’s profit $$P (in $$thousands of dollars) is modeled by the function $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$18$$ thousand dollars at $$x = 2$$ thousand units

Question 3

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 4

If $$f(x) = 3x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$5$$

Question 5

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 1$$ second

Question 6

Which of the following is the inverse function of $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 5}{2}$$

Question 7

Solve for $$x$$: $$\log_{2}(x) = 5.$$

Accepted Answer

$$x = 32$$

Question 8

A radioactive substance decays according to $$A(t) = 100e$$^{-0.3t}$$, where A$ is the amount remaining after t$ years. How much remains after 5$ years (rounded to the nearest whole number)?

Accepted Answer

$$22$$

Question 9

Which of the following equations represents a line parallel to $$y = 3x - 7$$?

Accepted Answer

$$y = 3x + 2$$

Question 10

If $$f(x) = x^2$ - 4x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -1)$$

Question 11

A population of bacteria doubles every 3 hours. If the initial population is 500, what is the population after 9 hours?

Accepted Answer

$$4000$$

Question 12

Which of the following is the solution to the system: $$2x + 3y = 7$$ and $$x - y = 1$$?

Accepted Answer

$$(2, 1)$$

Question 13

Which of the following is the domain of the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$x 
eq 4$$

Question 14

If $$f(x) = \sqrt{x-1}$$, for which values of $$x is$$ $$f(x)$$ defined?

Accepted Answer

$$x \geq 1$$

Question 15

A car depreciates in value by $$15\%$$ each year. If the car is worth $$20,000$$ now, what will it be worth after $$2$$ years? (Round to the nearest dollar.)

Accepted Answer

$$14,450$$

Question 16

Which of the following is the solution to $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 17

Which of the following is the correct solution for $$x in $$the equation $$\frac{3}{x} = 6$$?

Accepted Answer

$$x = 0.5$$

Question 18

If $$f(x) = 2x^2$ - 8x + 6$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-2$$

Question 19

A loan of $$5000 is $$made at an annual interest rate of $$6\%$$ compounded annually. What is the amount owed after $$3$$ years? (Round to the nearest dollar.)

Accepted Answer

$$5,955$$

Question 20

Which of the following is the range of the function $$f(x) = x^2$ + 4$$?

Accepted Answer

$$[4, \infty)$$

MAT137 Fall 2025 Course Schedule and Chapter Overview

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