Graphing Polynomial Functions

Question 1

Complete the statements about the key features of the graph of f(x) = x5 – 9x3.As x goes to negative infinity, f(x) goes to infinity, and as x goes to positive

Revolt · Accepted Answer

Part 1: negative; infinity, f(x) goes to: positive; negative

Question 2

infinity, f(x) goes to infinity.

Revolt · Accepted Answer

positive

Question 3

The graph of f(x) touches but does not crosscrossesneither crosses nor touches the x-axis at x = –3, 0, and 3.

Revolt · Accepted Answer

crosses

Question 4

Check all the statement(s) that are true about the polynomial function graphed. Its leading coefficient is positive.Its leading coefficient is negative.It has an odd degree.It has an even degree.It has exactly two real zeroes.It has exactly three real zeroes.None of the zeroes have even multiplicity.None of the zeroes have odd multiplicity.

Revolt · Accepted Answer

Its leading coefficient is negative.; It has an odd degree.; It has exactly three real zeroes.; None of the zeroes have even multiplicity.

Question 5

The zero [___] has a multiplicity of 1.

Revolt · Accepted Answer

Part 1: 1; Part 2: 2; 1

Question 6

of odd multiplicityof even multiplicity

Revolt · Accepted Answer

of even multiplicity; Selection 1: of even multiplicity; Selection 2: of odd multiplicity

Question 7

The zeroes of the function are -2 and 00 and 4-2, 0, and 4.

Revolt · Accepted Answer

-2, 0, and 4

Question 8

Let a and b be real numbers, where Which of the following functions could represent the graph on the right?

Revolt · Accepted Answer

f(x) = x (x – a)(x – b)2

Question 9

Explain how to sketch a graph of the function f(x) = x3 + 2x2 – 8x. Be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.

Revolt · Accepted Answer

The function factors as f(x) = x(x + 4)(x - 2), so its zeros are -4, 0, and 2, each with multiplicity 1. Since it is an odd-degree function with a positive leading coefficient, the graph falls to the left and rises to the right. It is negative on (-∞, -4) and (0, 2), and positive on (-4, 0) and (2, ∞). The graph crosses the x-axis at each zero.

Question 10

The graph touches, but does not cross, the x–axis at x = [___].

Revolt · Accepted Answer

Part 1: 4; Part 2: 0; 4

Graphing Polynomial Functions Answers

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