Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following is the correct solution set for the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 2 \pm \sqrt{2}$$

Question 2

A ball is thrown upward from the top of a 50-meter building with an initial velocity of 20 m/s. Its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 50. $$After how many seconds does the ball hit the ground?

Accepted Answer

$$t = 5.72$$

Question 3

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

Accepted Answer

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

Question 4

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$20 at$$ $$x = 3$$ thousand units

Question 5

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 6

If $$f(x) = x^2$ + 2x$$ and $$g(x) = 3x - 1$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 49$$

Question 7

A population of bacteria triples every 4 hours. If the initial population is 200, what will the population be after 12 hours?

Accepted Answer

$$200 	imes 3^3$ = 5400$$

Question 8

Which of the following is the solution to the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 9

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. Which function models the total cost $$C$$ for driving $$x$$ miles?

Accepted Answer

$$C(x) = 0.2x + 30$$

Question 10

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 11

If $$\log_2$(x) = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 12

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How much remains after 20 years (rounded to the nearest whole number)?

Accepted Answer

$$37$$

Question 13

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

Question 14

Which of the following is the domain of the function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

$$x 
eq 3, x 
eq -3$$

Question 15

A triangle has sides of length 7, 24, and 25. What is the area of the triangle?

Accepted Answer

$$84$$

Question 16

If $$f(x) = \sqrt{x-2}$$, what is the range of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 17

A medication is administered at a dose of 100 mg and decreases by 30% every hour. What is the amount remaining after 3 hours?

Accepted Answer

$$34.3 mg$$

Question 18

Which of the following is the solution to the equation $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2} \ln 7$$

Question 19

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

Accepted Answer

$$13$$

Question 20

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

Accepted Answer

$$x = -1, x = -5$$

Syllabus and Course Structure: College Algebra (Math 1030), Fall 2025

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