Q: Which of the following best describes the end behavior of the polynomial $$f(x) = x^2$ + 8x^2$ + 11x - 29$$?

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

Q: If $$f(x) = x^2$ and g(x) = 2x$, what is (f + g)(3$$)$$?

$$(f + g)(3) = 3^2$ + 2 \times 3 = 9 + 6 = 15$$

Q: A car's value depreciates according to $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years. What is the value after 3 years?

$$20000 \times (0.85)^3$ \approx 12262.5$$

Question 1

Given the quadratic function $$f(x) = x^2$ + 8x^2$ + 11x - 29$$, what is the value of $$f(2)$$?

Accepted Answer

$$f(2) = 2^2$ + 8(2^2$) + 11(2) - 29 = 4 + 32 + 22 - 29 = 29$$

Question 2

Suppose you use the Rational Root Theorem to find possible rational roots of $$f(x) = x^2$ + 8x^2$ + 11x - 29. $$Which of the following is a possible rational root?

Accepted Answer

$$x = \pm1$$

Question 3

Which of the following best describes the end behavior of the polynomial $$f(x) = x^2$ + 8x^2$ + 11x - 29$$?

Accepted Answer

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

Question 4

Given the function $$f(x) = \dfrac{8x}{x^2$ - 11}$$, which of the following is a vertical asymptote?

Accepted Answer

$$x = \sqrt{11}$$ and $$x = -\sqrt{11}$$

Question 5

For the rational function $$f(x) = \dfrac{8x}{x^2$ - 11}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 6

A company models its profit $$P as a $$function of units sold $$x by$$ $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit, and at how many units sold does it occur?

Accepted Answer

Maximum profit is $$P(10) = 100 at$$ $$x = 10$$ units

Question 7

Given $$f(x) = x^2$ - 4x + 3$$, which of the following is the correct factorization?

Accepted Answer

Question 8

Suppose $$f(x) = x^2$ - 4x + 3$$ and $$g(x) = x - 2. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (x - 2)^2$ - 4(x - 2) + 3$$

Question 9

A population of bacteria doubles every hour. If the initial population is 100, what is the population after 5 hours?

Accepted Answer

$$100 	imes 2^5$ = 3200$$

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 13

A ball is thrown upward with an initial velocity of 20 m/s from a height of 2 m. Its height after $$t$$ seconds is $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

Maximum height is $$h(2.04) \approx 22.4 m$$

Question 14

Which of the following is the correct domain of $$f(x) = \dfrac{1}{x - 3}$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 15

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

Accepted Answer

$$(f + g)(3) = 3^2$ + 2 	imes 3 = 9 + 6 = 15$$

Question 16

A car's value depreciates according to $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years. What is the value after 3 years?

Accepted Answer

$$20000 	imes (0.85)^3$ \approx 12262.5$$

Question 17

Which of the following is the correct solution to $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 18

If $$f(x) = \dfrac{x^2$ - 9}{x - 3}$$, what is $$f(3)$$?

Accepted Answer

$$f(3) is $$undefined

College Algebra: Midterm Exam 3 Sample Questions Study Guide

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