Question 1

Given the points $$(-9, 3)$$ and $$(-7, -5)$$, what is the equation of the line passing through them in slope-intercept form?

Accepted Answer

$$y = -4x -33$$

Question 2

A business’s revenue increases linearly with time. If the slope is $$8$$ and the y-intercept is $$4$$, which equation models the revenue $$y as a $$function of time $$x$$?

Accepted Answer

$$y = 8x + 4$$

Question 3

Which of the following is the correct slope-intercept equation for a line with slope $$\frac{1}{2}$$ and y-intercept $$2$$?

Accepted Answer

$$y = \frac{1}{2}x + 2$$

Question 4

Simplify the rational expression $$\frac{q^2$ - 4}{q^2$ - 4q + 4} to $$lowest terms.

Accepted Answer

$$\frac{q + 2}{q - 2}$$

Question 5

Reduce the rational expression $$\frac{3t^2$ + 21t + 30}{9t^2$ - 18t - 72} to $$lowest terms.

Accepted Answer

$$\frac{t + 5}{3(t - 4)}$$

Question 6

For the exponential function $$f(x) = 4^x - 6$$, what is the domain, range, y-intercept, and equation of the horizontal asymptote?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$(-6, \infty)$$; y-intercept: $$-5$$; Asymptote: $$y = -6$$

Question 7

For the function $$f(x) = \frac{1}{3^x} + 6$$, what is the domain, range, y-intercept, and equation of the horizontal asymptote?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$(6, \infty)$$; y-intercept: $$7$$; Asymptote: $$y = 6$$

Question 8

Rewrite $$\log_b x^4$ y^5$ z as a $$sum or difference of multiples of logarithms.

Accepted Answer

$$4 \log_b x + 5 \log_b y + \log_b z$$

Question 9

Express $$\log_b \frac{x y^3$}{w^3$ z} as a $$sum and/or difference of logarithms.

Accepted Answer

$$\log_b x + 3 \log_b y - 3 \log_b w - \log_b z$$

Question 10

A company’s cost function is $$f(x) = 6x - 9. $$What is the y-intercept and what does it represent in a real-world context?

Accepted Answer

Y-intercept: $$-9$$; It represents the fixed cost when no units are produced.

Question 11

For the function $$f(x) = \frac{x - 7}{2}$$, what is the slope and y-intercept?

Accepted Answer

Slope: $$\frac{1}{2}$$; y-intercept: $$-\frac{7}{2}$$

Question 12

What is the domain of the function $$y = \frac{12}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 13

Which graph best represents the function $$y = -4x$$?

Accepted Answer

A straight line with negative slope passing through the origin

Question 14

A company’s profit is modeled by $$P(x) = 8x + 4$$, where $$x is $$the number of units sold. If the company sells $$10$$ units, what is the profit?

Accepted Answer

$$84$$

Question 15

If the function $$f(x) = 4^x - 6$$ models the population of bacteria after $$x$$ hours, what is the population at $$x = 0$$?

Accepted Answer

$$-5$$

Question 16

Which of the following best describes the horizontal asymptote of $$f(x) = \frac{1}{3^x} + 6$$?

Accepted Answer

$$y = 6$$

Question 17

A business’s cost function is $$C(x) = 6x - 9. If $$the cost for producing $$5$$ units is $$C(5)$$, what is the value?

Accepted Answer

$$21$$

Question 18

If $$y = 8x + 4$$ represents the revenue function, what is the slope and what does it mean in a business context?

Accepted Answer

Slope: $$8$$; It represents the rate of change of revenue per unit sold.

Business Calculus Chapter 3 Skills Review Guidance

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