AP Precalculus (1.7-2.2) Quiz 3 Study Guide

​AP Precalculus (1.7-2.2) Quiz 3 Study Guide

​"You can't compromise your education. You have to wise up and make your grade rise so that you can receive the ultimate prize."
BY Mr. C and Ms. G

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Multiple Choice

Which of the following functions will have a horizontal asymptote at  $$y=\frac{2}{3}$$  ? #1

• $$f\left(x\right)=\frac{2x^5}{3x^2-1}$$  

• $$f\left(x\right)=\frac{x+2x^2+4}{5+2x\ +3x^2}$$  

• $$f\left(x\right)=\frac{-2x^3+1}{3x^3-x^2-1}$$  

• $$f\left(x\right)=\frac{2x^5+1}{3x^4+3x^2+2}$$  

Match

Match the following: #3

• $$f\left(x\right)=\frac{6}{x-1}$$

• $$f\left(x\right)=\frac{x+4}{x-5}$$

• $$f\left(x\right)=\frac{-3x-1}{3x+2}$$

• $$f\left(x\right)=\frac{6x+1}{3x-5}$$

• $$f\left(x\right)=\frac{-8x+3}{4x}$$

H.A. at x-axis.

H.A. at y = 1

H.A. at y = -1

H.A. at y = 2

H.A. at y = -2

• H.A. at x-axis.

• H.A. at y = 1

• H.A. at y = -1

• H.A. at y = 2

• H.A. at y = -2

Match

Match the following: #4

• $$f\left(x\right)=\frac{6}{x-1}$$

• $$f\left(x\right)=\frac{x+4}{x-5}$$

• $$f\left(x\right)=\frac{-3x-1}{3x+2}$$

• $$f\left(x\right)=\frac{6x+1}{3x-5}$$

• $$f\left(x\right)=\frac{-8x+3}{4x}$$

V.A. at x = 1

V.A. at x = 5

V.A. at x = -2/3

V.A. at x = 5/3

V.A. at x = 0

• V.A. at x = 1

• V.A. at x = 5

• V.A. at x = -2/3

• V.A. at x = 5/3

• V.A. at x = 0

Multiple Choice

What is the x-value of the point of discontinuity (the hole)? #5

• x=2

• x=2 and x=3

• x=-3

• x=3

Multiple Choice

Find the vertical asymptotes of the function: #7

$$f\left(x\right)=\frac{2x^2+4x-6}{x^2-5x+6}$$  

• $$x=2,3$$  

• $$x=-3,-2$$  

• $$x=-3,1$$  

• None

Multiple Select

$$y=\frac{x^2-4x+3}{2x^2-2x}$$  

Select ALL the following statements that are true. #11

• Vertical asymptote at x = 1

• Vertical asymptote at x=0

• Horizontal asymptote at y = 1/2

• Hole at (-1, 2)

• Hole at (1, -1)

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Multiple Choice

​The polynomial function  $$p$$  is given by $$p\left(x\right)=\left(x+2\right)^4$$  . Which of the following expressions is equivalent to $$\left(x+2\right)^4$$   ? #12

• $$x^4+2x^3+4x^2+8x+16$$

• $$x^4+4x^3+6x^2+4x+1$$

• $$x^4+8x^3+24x^2+32x+16$$

• $$2x^4+8x^3+12x^2+8x+2$$

Multiple Choice

What is the coefficient of x⁶ if the expression (x+4)⁸ is expanded? #13

• 16

• 448

• 114,688

• 322,560

Multiple Choice

Find the domain of $$f\left(x\right)=\frac{x^2-3x}{x^2-2x}$$  . #17

• (-∞, 0)U(0,2)U(2,∞)

• (-∞, -2)U(-2,0)U(0,∞)

• All real numbers

• Hint: The domain is not all Real Numbers bc there is a HOLE and a Vertical Asymptote. Find the Hole and Vertical Asymptote and exclude those values.

Multiple Choice

What is the slant asymptote for the function? #18

• y = 12

• y = x - 5

• y = x-5 + 12/(x+2)

• y = 12/(x+2)

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Multiple Choice

What are the solutions for the polynomial inequality? $$-2\left(x+5\right)\left(x-2\right)\left(x-3\right)\ge0$$   #24
  

•   $$\left(-5,2\right)\cup\left(3,\infty\right)$$  

• $$\left[-5,2\right]\cup\left[3,\infty\right)$$  

• $$\left(-\infty,\ -5\right)\cup\left(2,3\right)$$  

• $$\left(-\infty,-5\right]\cup\left[2,3\right]$$  

Multiple Choice

Find all of the zeros of the polynomial function P(x):
P(x) = x⁵ - 6x³ + 5x #26

• $$0;\pm1;\pm5$$

• $$0;1;\pm\sqrt[]{5}$$

• $$0;\pm1;5$$

• $$0;\pm1;\pm\sqrt[]{5}$$

Multiple Choice

Solve:   m³ + 2m² - 16m - 32 = 0 #27

• 2; ±4

• -2; ±6

• -2; ±4

• 2; ±6

Fill in the Blank

Ryan has 3000 feet of fencing to enclose a rectangular field for his horses. One side of the field

lies along the river, so only three sides require fence material.

A. Express the area A of the rectangle as a function of the width x of the rectangle. #30

(

)

=

-

(

/

)

^

Multiple Choice

Write the first five terms of the sequence. (Assume that n begins with 1.) #31
$$a_n=-7n+8$$

• 1, –14, –21, –28, –35

• 1, –6, –13, –20, –27

• 1, 9, 17, 25, 33

• 
  8, 1, –6, –13, –20

Multiple Choice

Given the rule:  a_n = 7(½)^n-1
Identify the first term. #35

• a_n
• 7
• ½
• n

Multiple Choice

Given the rule:  a_n = 7(½)^n-1
Identify the common ratio. #36

• a_n
• 7
• ½
• n-1

Multiple Choice

Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ? #32

• a_n = a_n-1 x 3
• a_n = 5(3)^n-1
• a_n = 3(5)^n-1
• a_n = 5 + (n-1)3

Multiple Choice

Given a geometric sequence where a₃ = 320 and a₆ = 20480, find a_8. #38

• 4
• 20
• 16,384
• 327,680

Multiple Choice

A person travels by car.  They record their miles driven in a data table.  Calculate the linear regression equation of this data. #46

• y = 61.93x - 1.79
• y = -1.79x + 61.93
• y = 0.016x + 0.03
• y = 0.03x + 0.016

Multiple Choice

What equation best represents this data set?

{(−4, −5), (−3, −8), (−2, −9), (−1, −8), (0, −5), (1, 0.5)} #40

• $$y=1.04x\ +4.84$$

• $$y=1.04x-4.84$$

• $$y=1.04x^2+4.21x-4.84$$

• $$y=1.04x^2+4.21x+4.84$$

Multiple Choice

Find the best fitting quadratic model for the data given. #41

• $$1.2x^2+13x+504.3$$

• $$12x^2+13x+504.3$$
  

• $$0.12x^2+1.3x+504.3$$
  

Multiple Choice

Use the exponential regression to find an equation that fits the data, where x is the years since 1990. #44

• y=8.92•1.23^x
• y=1.23•8.92^x
• y=8.92+1.23x
• y=8.92x+1.23