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?

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

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