Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{(-6,7),\ (-2,-8),\ (4,-5),\ (4,6)\}$$

Question 2

Given the function $$f(x) = x^2$ - 5x + 1$$, what is $$f(-4)$$?

Accepted Answer

$$37$$

Question 3

Find the domain of the function $$f(x) = \dfrac{x}{x-8}.$$

Accepted Answer

$$(-\infty, 8) \cup (8, \infty)$$

Question 4

A real estate agent receives a commission of $27,075 on the sale of a home at a 15% commission rate. What was the sale price of the home?

Accepted Answer

$$180,500$$

Question 5

Given the linear regression equation $$y = 67.3 + 1.07x$$ for predicting test scores $$y$$ based on hours studied $$x$$, what is the predicted score for a student who studies 4 hours?

Accepted Answer

$$71.6$$

Question 6

Solve the equation $$\dfrac{2}{3}x - \dfrac{1}{2} = \dfrac{1}{6}x - \dfrac{1}{4}.$$

Accepted Answer

$$\dfrac{1}{2}$$

Question 7

Write the equation of the line in slope-intercept form that passes through $$(2,2)$$ with slope $$m = -\dfrac{3}{4}.$$

Accepted Answer

$$y = -\dfrac{3}{4}x + \dfrac{7}{2}$$

Question 8

If the current $$I in an $$electrical conductor varies inversely as the resistance $$R$$, and $$I = 5$$ amperes when $$R = 762$$ ohms, what is the current when $$R = 462$$ ohms?

Accepted Answer

$$8.2$$ amperes

Question 9

The distance $$d$$ required to stop a car varies directly as the square of its speed $$v. If it $$takes $$112$$ feet to stop at $$40$$ mph, how far to stop at $$62$$ mph?

Accepted Answer

$$269.08$$ feet

Question 10

Given $$f(x) = 8x - 3$$ and $$g(x) = 2x - 4$$, find $$(f-g)(x).$$

Accepted Answer

$$6x + 1$$

Question 11

For $$f(x) = 5 - 7x^3$, find and simplify the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$.

Accepted Answer

$$-7(3x^2 + 3xh$$ + $$h^2$$)$$

Question 12

Which of the following equations represents a function whose graph is the graph of $$y = x^3$ shifted 4.3$ units to the right and vertically shrunk by a factor of 0.8$?

Accepted Answer

$$f(x) = 0.8(x - 4.3)^3$

Question 13

Given $$f(x) = -4x - 8$$ and $$g(x) = 5x^2$ + 5x - 8$$, find $$(f \circ g)(-8).$$

Accepted Answer

$$-1096$$

Question 14

Determine algebraically whether the graph of $$xy = -2 is $$symmetric with respect to the x-axis, y-axis, or the origin.

Accepted Answer

Origin only

Question 15

If the number $$G of $$gears a machine can make varies directly as the time $$T it $$operates, and it can make $$3230$$ gears in $$18$$ hours, how many gears can it make in $$12$$ hours?

Accepted Answer

$$2153.33$$

Question 16

Given $$f(x) = -2x + 7$$ and $$g(x) = 3x + 8$$, find $$(g \circ f)(x).$$

Accepted Answer

$$-6x + 29$$

Question 17

For the function $$f(x) = x^3$ - 3x^2$ + 1$$, which of the following is true about its relative extrema and intervals of increase/decrease?

Accepted Answer

Relative maximum at $$x=0 ($$value $$1$$), relative minimum at $$x=2 ($$value $$-3$$), increasing on $$(-\infty, 0)$$ and $$(2, \infty)$$, decreasing on $$(0, 2)$$

Question 18

Given the cost function $$C(x) = R(x) - P(x)$$, where $$R(x) = 57x - 0.3x^2$ and P(x$$) = $$-0.3x^2 + 45x - 8$, find C(x$$)$$.

Accepted Answer

$$12x + 8$$

Question 19

Which point is symmetric to $$(1.5, 1.75)$$ with respect to the y-axis?

Accepted Answer

$$(-1.5, 1.75)$$

Precalculus Chapter 1 & 2 Study Guide: Functions, Graphs, and Linear Equations

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