AP Precalculus 1.4-1.7 Study Guide Lesson

​Study Guide 1.4-1.7 Lesson

​1.6 HW 1.7 HW

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Multiple Choice

One zero of 2x³-13x²+36 is 2. #1
What is another zero?

• 3/2
• 6
• 2
• -6

Multiple Choice

Find all real solutions of the polynomial equation x³ - 3x² - 2x + 4 = 0. #2

• x = -1, 1 ± √5
• x = 1, 1 + √5
• x = 2, 1 ± √5
• x = 1, 1 ± √5

Multiple Choice

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing. #5

• True
• False, because the solution and root are the same but the x-intercept and zero are different
• False, because the x-intercept and root are the same but the zero and solution are different
• False, they are all different

Multiple Choice

How many real zeros exist for the polynomial? #6

• 2
• 1
• 4
• None

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Multiple Choice

Based on the graph (picture), Determine the behavior of the function. #10

• The leading coefficient of polynomial is positive and degree of the polynomial is even.

• The leading coefficient of the polynomial is negative and degree of the polynomial is even.

• The leading coefficient of the polynomial is negative and degree of the polynomial is odd.

• The leading coefficient of the polynomial is positive and degree of the polynomial is odd.

Multiple Choice

Determine end behavior of function with the given graph. #11

• $$f\left(x\right)\ \rightarrow\ -\infty\ as\ x\rightarrow-\infty$$   $$f\left(x\right)\rightarrow+\infty\ as\ x\rightarrow+\infty$$  

• $$f\left(x\right)\rightarrow+\infty\ as\ x\ \rightarrow-\infty$$     $$f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow+\infty$$  

•    $$f\left(x\right)\rightarrow-\infty\ as\ x\ \rightarrow-\infty$$   $$f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow+\infty$$  

•   $$f\left(x\right)\rightarrow+\infty\ as\ x\rightarrow-\infty$$   $$f\left(x\right)\rightarrow+\infty\ as\ x\rightarrow+\infty$$  

Multiple Choice

Determine the remaining zeros of f if: #15

f(x) = x³ - 3x² + 4x - 12; Zeros: -2i

• x = 3, 2i

• x = -3

• x = 2i

• x = -3, 2i

Multiple Choice

Determine the remaining zeros of f if: #16

f(x) = x³ - 5x² + 7x + 13; Zeros: 3-2i

• x = 1, 3+2i

• x = -3+2i

• x = -1

• x = -1, 3+2i

Multiple Choice

Determine the polynomial function of degree 5 whose coefficients are real numbers and has the zeros: 1 (mult 3), and 4-i. #19

• f(x) = (x - 1)³(x - 4 + i)(x - 4 - i)

• f(x) = (x - 1)(x - 4 + i)

• f(x) = (x - 1)(x - 4 - i)

• f(x) = (x + 1)³(x - 4 + i)(x - 4 - i)

Match

Match the following. #20

Quadratic

Cubic

Linear

Quartic

Quintic

• Quadratic

• Cubic

• Linear

• Quartic

• Quintic

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Multiple Choice

How many vertical asymptotes does f(x) have? #24

• None

• 1

• 2

• 3

Multiple Choice

Which asymptotes are determined by looking at the denominator of a function? #26

• vertical
• horizontal
• slant
• none

Multiple Choice

Find the horizontal asymptote of f(x). #25

• None

• y=6

• y=1/3

• y=3

Multiple Choice

What is the equation of the slant asymptote? #29

• y = x + 1

• y = x + 2

• y = x + 3

• y = x

Multiple Choice

What are the x and y intercepts? #32

• (4, 0) and (0, -4)

• (-4, 0) and (0, -4)

• (-4, 0) and (0, 4)

• (0, 0) and (0, -4)

Multiple Choice

What is the x-coordinate of the hole, if one exists? #33

• -4

• -3

• 3

• there isn't one