Question 1

Which of the following is the correct factorization of the quadratic $6x^2 + 7x + 2$?

Accepted Answer

$(3x+2)(2x+1)$

Question 2

A line passes through the points $(0,3)$ and $(4,7)$. What is its equation in slope-intercept form?

Question 3

Given the quadratic function $f(x) = 2(x-5)^2 + 3$, what is the vertex of the parabola?

Accepted Answer

$(5, 3)$

Question 4

Which of the following is a correct description of a piecewise function?

Accepted Answer

A function defined by different expressions over different intervals of its domain.

Question 5

For the rational function $f(x) = \frac{x^2}{x^2-4}$, what is the vertical asymptote?

Accepted Answer

$x = 2$ and $x = -2$

Question 6

Calculate the difference quotient for $f(x) = 3x^2$.

Accepted Answer

$6x + 3h$

Question 7

What is the domain of the exponential function $f(x) = 2^x$?

Accepted Answer

$(-\infty, \infty)$

Question 8

Suppose the supply equation is $p = 0.04x + 4$ and the demand equation is $p = -0.02x + 10$. What is the equilibrium quantity?

Accepted Answer

$100$

Question 9

Given the function $f(x) = \frac{2x+1}{x-2}$, what is the horizontal asymptote?

Accepted Answer

$y = 1$

Question 10

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

Accepted Answer

$x^2 - 2x$

Question 11

A loan of $50,000$ at $6\%$ annual interest, paid monthly over $2$ years, has a monthly payment calculated by $PMT = \frac{P r}{1-(1+r)^{-n}}$. What is the value of $r$?

Accepted Answer

$0.005$

Question 12

Which of the following best describes the range of the logarithmic function $f(x) = \ln(x)$?

Accepted Answer

$(-\infty, \infty)$

Question 13

If $f(x) = x^2$ and $h = 2$, what is the value of the difference quotient $\frac{f(x+h)-f(x)}{h}$?

Accepted Answer

$2x + 2$

Question 14

Which of the following is the correct vertex form for a quadratic function?

Accepted Answer

$f(x) = a(x-h)^2 + k$

Question 15

If the degree of the numerator and denominator of a rational function are equal, what is the horizontal asymptote?

Accepted Answer

The ratio of the leading coefficients.

Question 16

Which of the following is NOT a property of exponential functions?

Accepted Answer

The range is $(-\infty, \infty)$.

Question 17

A company’s revenue is modeled by $R(x) = 100x - 0.5x^2$. What is the maximum revenue, and at what quantity $x$ does it occur?

Accepted Answer

Maximum at $x = 100$, $R(100) = 5000$

Question 18

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

Accepted Answer

$(x+1)^2$

Question 19

Which of the following is the correct formula for compound interest?

Accepted Answer

$A = P(1 + r/n)^{nt}$

Question 20

If the supply and demand equations are $p = 0.05x + 2$ and $p = -0.03x + 10$, what is the equilibrium price?

Accepted Answer

$p = 6$

Business Calculus: Core Algebra and Applications Study Guide

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