AnswersAlgebra IIPolynomial Functions

Practice Test Answers

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1
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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 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 .
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 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 .
2
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The polynomial function f of x is equal to 3 x to the 5th power minus 2 x squared plus 7 x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground level? Begin by factoring x to create a constant term.

A
0 , plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
B
plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , plus or minus 3
C
0 , plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , 3
D
plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
4

If open paren x minus 5 close paren is a factor of f of x , which of the following must be true?

A
A root of f of x is x is equal to 5 .
B
A root of f of x is x is equal to negative 5 .
C
Both x is equal to negative 5 and x is equal to 5 are roots of f of x .
D
Neither x is equal to negative 5 nor x is equal to 5 is a root of f of x .
6

What is the end behavior of the graph of the polynomial function f of x is equal to negative x to the 5th power plus 9 x to the 4th power minus 18 x cubed ?

A
As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow negative infinity .
B
As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow infinity .
C
As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow infinity .
D
As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow negative infinity .
8

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 minus 15 x plus 12
B
f of x is equal to 3 x squared plus 15 x plus 12
C
f of x is equal to 3 x squared minus 5 x plus 4
D
f of x is equal to 3 x squared plus 5 x plus 4
10

Which polynomial function could be represented by the graph?

A
f of x is equal to 2 x squared minus 2 x minus 4
B
f of x is equal to x squared plus x minus 2
C
f of x is equal to 2 x squared plus 2 x minus 4
D
f of x is equal to x squared minus x minus 2
11

Let A and b be real numbers where A is not equal to b is not equal to 0 Which of the following functions could represent the graph?

A
f of x is equal to x open paren x minus A close paren squared open paren x minus b close paren to the 4th power
B
f of x is equal to x open paren x minus A close paren cubed open paren x minus b close paren squared
C
f of x is equal to x squared open paren x minus A close paren to the 5th power open paren x minus b close paren
D
f of x is equal to x to the 4th power open paren x minus A close paren open paren x minus b close paren squared
12

Which expression is a possible leading term for the polynomial function graphed?

A
negative 18 x to the 14th power
B
negative 10 x to the 7th power
C
17 x to the 12th power
D
22 x to the 9th power

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