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Graphing Polynomial Functions Answers

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At which root does the graph of f(x) = (x + 4)6(x + 7)5 cross the x-axis?

A
–7
B
–4
C
4
D
7
2
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Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

Question illustration
A
f(x) = x(x – a)3(x – b)3
B
f(x) = (x – a)2(x – b)4
C
f(x) = x(x – a)6(x – b)2
D
f(x) = (x – a)5(x – b)
3

What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?

A
As , and as , .
Option A
B
As , and as , .
Option B
C
As , and as , .
Option C
D
As , and as , .
Option D
4

At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x-axis?

A
–5
B
–2
C
2
D
5
5

Which of the following graphs could be the graph of the function f(x) = x4 + x3 – x2 – x?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

A polynomial function has a root of –5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree, which statement about the graph is true?

A
The graph of the function is positive on (, –5).
Option A
B
The graph of the function is negative on (–5, 3).
C
The graph of the function is positive on (, 1).
Option C
D
The graph of the function is negative on (3, ).
Option D
7

Which statement describes the graph of f(x) = –x4 + 3x3 + 10x2?

A
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5 and x = –2.
B
The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = –2.
C
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5 and x = 2.
D
The graph touches the x-axis at x = 0 and crosses the x-axis at x = –5 and x = 2.
8

Which graph shows the same end behavior as the graph of f(x) = 2x6 – 2x2 – 5?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

Which of the following graphs could be the graph of the function ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

A polynomial function has a root of –4 with multiplicity 4, a root of –1 with multiplicity 3, and a root of 5 with multiplicity 6. If the function has a positive leading coefficient and is of odd degree, which could be the graph of the function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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