AnswersAlgebra IIFunctions: Part Three

Practice Test Answers

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1
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What are the solutions of the equation x to the 4th power minus 5 x squared minus 36 is equal to 0 ? Use factoring to solve.

A
x is equal to plus or minus 2 and x is equal to plus or minus 3
B
x is equal to plus or minus 2 and x is equal to plus or minus 3 i
C
x is equal to plus or minus 2 i and x is equal to plus or minus 3
D
x is equal to plus or minus 2 i and x is equal to plus or minus 3 i
2
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If 5 plus 6 i is a root of the polynomial function f of x , which of the following must also be a root of f of x ?

A
negative 5 minus 6 i
B
5 minus 6 i
C
6 plus 5 i
D
6 minus 5 i
3

Which graph represents y is equal to cube root of x plus 2 ?

A
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. A graph of cubic function passes through points (negative 8 comma 0), (0 comma 2), and (8 comma 4). The curve has a point of inflection at (0 comma 2).
B
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 8 to 8 by twos with grid lines every 1 unit. An S-shaped curve crosses the horizontal axis at 2 comma 0 and crosses the vertical axis near 0 comma negative 1.3. The curve extends to the left ending in an arrow near negative 9 comma negative 2.2, and extends to the right ending in an arrow near 9 comma 2.
C
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 8 to 8 by twos with grid lines every 1 unit. An S-shaped curve crosses the vertical axis at 0 comma negative 2 and crosses the horizontal axis at 8 comma 0. The curve extends to the left ending in an arrow near negative 9 comma negative 4, and extends to the right ending in an arrow near 9 comma 0.3.
D
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 8 to 8 by twos with grid lines every 1 unit. An S-shaped curve crosses the horizontal axis at negative 2 comma 0 and crosses the vertical axis near 0 comma 1.3. The curve extends to the left ending in an arrow near negative 9 comma negative 1.5, and extends to the right ending in an arrow near 9 comma 2.2.
4

Which second degree polynomial function f of x has a leading coefficient of 3 and roots 4 and 1 ?

A
f of x is equal to 3 x squared plus 15 x plus 12
B
f of x is equal to 3 x squared minus 5 x plus 4
C
f of x is equal to 3 x squared minus 15 x plus 12
D
f of x is equal to 3 x squared plus 5 x plus 4
5

What are the vertical and horizontal asymptotes for the function f of x is equal to the fraction with numerator x squared plus x minus 6 and denominator x cubed minus 1 ?

A
vertical asymptote: x is equal to negative 2 , x is equal to 3 horizontal asymptote: y is equal to 0
B
vertical asymptote: x is equal to 1 horizontal asymptote: y is equal to 0
C
vertical asymptote: x is equal to 1 horizontal asymptote: none
D
vertical asymptote: x is equal to negative 2 , x is equal to negative 3 horizontal asymptote: none
6

Which statement describes the graph of this polynomial function? f of x is equal to x to the 4th power plus x cubed minus 2 x squared

A
The graph touches the x -axis at x is equal to negative 2 and x is equal to 1 and crosses the x -axis at x is equal to 0 .
B
The graph crosses the x -axis at x is equal to 2 and x is equal to negative 1 and touches the x -axis at x is equal to 0 .
C
The graph crosses the x -axis at x is equal to negative 2 and x is equal to 1 and touches the x -axis at x is equal to 0 .
D
The graph touches the x -axis at x is equal to 2 and x is equal to negative 1 and crosses the x -axis at x is equal to 0 .
7

Which function has a domain of x is greater than or equal to 5 and a range of y is less than or equal to 3 ?

A
y is equal to square root of x plus 5 end root minus 3
B
y is equal to square root of x minus 5 end root plus 3
C
y is equal to negative square root of x minus 5 end root plus 3
D
y is equal to negative square root of x plus 5 end root minus 3
8

Which second degree polynomial function has a leading coefficient of 2 and roots negative 3 and 5 ?

A
f of x is equal to 2 x squared minus 2 x minus 15
B
f of x is equal to 2 x squared plus 4 x minus 30
C
f of x is equal to 2 x squared plus 2 x minus 15
D
f of x is equal to 2 x squared minus 4 x minus 30
9

For what values of A and m does f of x have a horizontal asymptote at y is equal to 2 and a vertical asymptote at x is equal to 1 ? f of x is equal to the fraction with numerator 2 x to the m th power and denominator x plus A

A
A is equal to 1 , m is equal to 0
B
A is equal to 1 , m is equal to 1
C
A is equal to negative 1 , m is equal to 1
D
A is equal to negative 1 , m is equal to 0
10

Which statement best describes the equation x to the 5th power plus x cubed minus 14 is equal to 0 ?

A
The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
B
The equation is quadratic in form because it is a fifth-degree polynomial.
C
The equation is quadratic in form because the difference of the exponent of the lead term and the exponent of the middle term is 2 .
D
The equation is not quadratic in form because the exponent of the lead term is not the square of the exponent of the middle term.

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Practice Test Answers — Algebra II