Question 1

Given the function $f(x) = x^3 - 6x^2 + 9x + 1$, which of the following intervals is where the function is decreasing?

Accepted Answer

$(1, 3)$

Question 2

Suppose a ball is thrown vertically upward from the top of a building 800 feet tall with an initial velocity of 80 feet per second. The distance $d(t)$ in feet of the ball from the ground after $t$ seconds is given by $d(t) = -16t^2 + 80t + 800$. What is the maximum height of the ball?

Accepted Answer

$1000$ feet

Question 3

Find the domain of the function $f(x) = \dfrac{2x}{x^2 - 9}$.

Accepted Answer

$x 
eq -3,\ 3$

Question 4

A radioactive substance decays according to the model $A(t) = Ae^{-0.07t}$, where $A$ is the initial amount present and $t$ is time in years. After how many years will 80\% of the original amount remain?

Accepted Answer

$t = 3.19$

Question 5

Which of the following is the correct sum of $\log(x) + \log(x-3)$ expressed as a single logarithm?

Accepted Answer

$\log(x(x-3))$

Question 6

Given $f(x) = x^4 - 9x$ and $g(x) = 2x + 3$, what is $f(g(x))$?

Accepted Answer

$(2x+3)^4 - 9(2x+3)$

Question 7

A company’s profit is modeled by $P(x) = -0.04x^2 + 90x - 300$, where $x$ is the number of items sold. What is the maximum profit, and how many items must be sold to reach it?

Accepted Answer

Maximum profit is $10125$ at $x = 1125$

Question 8

Which of the following functions is even?

Accepted Answer

$f(x) = x^4 + 5x^2$

Question 9

Solve for $x$: $6e^{x+9} = 30$

Accepted Answer

$x = \ln(5) - 9$

Question 10

Suppose a polynomial function of degree 4 with rational coefficients has zeros $-4$, $1$, and $2i$. What is the polynomial written as a product of linear factors?

Accepted Answer

$(x+4)(x-1)(x-2i)(x+2i)$

Question 11

A large group of students is asked to memorize a list of 60 Italian words. The number of words retained is modeled by $W(t) = 60e^{-0.2t}$, where $t$ is the number of hours after memorization. What is the horizontal asymptote for the graph of this function?

Accepted Answer

$y = 0$

Question 12

Given the piecewise-defined function $f(x) = \begin{cases} 2x+1 & x < -2 \ x^2 & x \geq -2 \end{cases}$, what is $f(-3)$?

Accepted Answer

$f(-3) = -5$

Question 13

Convert the equation $4^x = 2.8$ to a logarithmic equation.

Accepted Answer

$x = \log_4(2.8)$

Question 14

Which of the following is the correct expression for the difference quotient $\dfrac{f(x+h) - f(x)}{h}$ for $f(x) = x^2$?

Accepted Answer

$2x + h$

Question 15

A certain company has fixed costs of $1500 with a variable cost per unit of $22. The commodity is sold for $30$ per unit. Which equation represents the break-even point?

Accepted Answer

$1500 + 22x = 30x$

Question 16

Which of the following is the correct solution to $\log(x+1) - \log(x-3) = \log(2)$?

Accepted Answer

$x = 5$

Question 17

Given the function $f(x) = \dfrac{3x+1}{x-2}$, what is the equation of the vertical asymptote?

Accepted Answer

$x = 2$

Question 18

Which of the following is the correct inverse of $f(x) = 3x - 2$?

Accepted Answer

$f^{-1}(x) = \dfrac{x+2}{3}$

Question 19

If the graph of $f(x)$ is reflected over the y-axis and shifted 2 units down, what is the resulting function?

Accepted Answer

$f(-x) - 2$

College Algebra Final Exam Review: Comprehensive Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards