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?

Accepted Answer

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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