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

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

Question 1

Given the quadratic function $f(x) = x^2 + 8x^2 + 11x - 29$, use the Rational Root Theorem to determine which of the following could be a possible rational root.

Accepted Answer

$\frac{1}{1}$

Question 2

Suppose $f(x) = 2x^3 - 5x^2 + 4x - 8$. What is $f(2)$?

Accepted Answer

$0$

Question 3

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

Accepted Answer

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

Question 4

A company models its profit $P$ (in thousands of dollars) by $P(x) = -2x^2 + 12x - 16$, where $x$ is the number of units sold (in thousands). How many units should be sold to maximize profit?

Accepted Answer

$x = 4$

Question 5

Given the function $f(x) = \frac{2x+1}{x-3}$, which value of $x$ is NOT in the domain?

Accepted Answer

$x = 3$

Question 6

If $f(x) = x^2 - 4x + 7$, what is the vertex of the parabola?

Accepted Answer

$(2, 3)$

Question 7

Which of the following is the correct factorization of $x^2 - 5x + 6$?

Accepted Answer

$(x-2)(x-3)$

Question 8

A rational function $R(x)$ has a vertical asymptote at $x = 2$ and a horizontal asymptote at $y = 0$. Which of the following could be $R(x)$?

Accepted Answer

$R(x) = \frac{1}{x-2}$

Question 9

Given $f(x) = x^2 - 6x + 8$, find all real zeros.

Accepted Answer

$x = 2, x = 4$

Question 10

Suppose $f(x) = 3x^2 - 12x + 9$. What is the minimum value of $f(x)$?

Accepted Answer

$f(2) = -3$

Question 11

A population of bacteria is modeled by $P(t) = 500e^{0.2t}$, where $t$ is time in hours. What is the population after 5 hours?

Accepted Answer

$500e^{1}$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

$9$

Question 14

A ball is thrown upward with an initial velocity of 32 ft/s from a height of 48 ft. Its height after $t$ seconds is $h(t) = -16t^2 + 32t + 48$. When does the ball reach its maximum height?

Accepted Answer

$t = 1$ s

Question 15

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

Accepted Answer

$x = 6, x = -1$

Question 16

Given $f(x) = x^3 - 3x^2 + 2x$, which of the following is a local minimum?

Accepted Answer

$(2, -4)$

Question 17

A chemical reaction is modeled by $C(t) = 100 - 80e^{-0.5t}$, where $C$ is the concentration at time $t$. What is the initial concentration?

Accepted Answer

$C(0) = 20$

Question 18

Which of the following is the correct solution set for $x^2 - 9 = 0$?

Accepted Answer

$x = 3, x = -3$

Question 19

Suppose the graph of $y = f(x)$ is shown below and passes through $(0, 2)$, $(1, 4)$, $(2, 8)$, and $(3, 16)$. Which type of function best models this data?

Accepted Answer

Exponential

Question 20

A medical dosage is modeled by $D(t) = 50e^{-0.1t}$, where $t$ is time in hours. How long until the dosage drops below 10 mg?

Accepted Answer

$t > 16.1$ hours

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