Graphing Polynomial Functions

Question 1

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

Revolt · Accepted Answer

The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = –2.

Question 2

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?

Revolt · Accepted Answer

The graph of the function is negative on (3, ).

Question 3

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

Revolt · Accepted Answer

–2

Question 4

What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?

Revolt · Accepted Answer

As , and as , .

Question 5

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

Revolt · Accepted Answer

mc020-1.jpg

Question 6

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

Revolt · Accepted Answer

–7

Question 7

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

Revolt · Accepted Answer

mc003-1.jpg

Question 8

Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

Revolt · Accepted Answer

f(x) = (x – a)2(x – b)4

Question 9

Which graph has the same end behavior as the graph of f(x) = –3x3 – x2 + 1?

Revolt · Accepted Answer

mc004-4.jpg

Question 10

Which of the following describes the zeroes of the graph of f(x) = 3x6 + 30x5 + 75x4?

Revolt · Accepted Answer

–5 with multiplicity 2 and 0 with multiplicity 4

Graphing Polynomial Functions Answers

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