Graphing Polynomial Functions — Unit test

Question 1

If f(–5) = 0, what are all the factors of the function ? Use the Remainder Theorem.

Revolt · Accepted Answer

(x – 2)(x + 5)(x – 3)

Question 2

What are the solutions of the equation (x + 2)2 – 2(x + 2) – 15 = 0? Use u substitution to solve.

Revolt · Accepted Answer

x = –5 and x = 3

Question 3

Which statement best describes the equation x5 + x3 – 14 = 0?

Revolt · Accepted Answer

The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.

Question 4

What are the solutions of the equation x4 – 5x2 – 36 = 0? Use factoring to solve.

Revolt · Accepted Answer

x = ±2i and x = ±3

Question 5

Which best describes the end behavior of ?

Revolt · Accepted Answer

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.

Question 6

If (x – 5) is a factor of f(x), which of the following must be true?

Revolt · Accepted Answer

A root of f(x) is x = 5.

Question 7

Which is a factor of f(x) = 60x4 + 86x3 – 46x2 – 43x + 8? Use the Rational Root Theorem to help you find your answer.

Revolt · Accepted Answer

6x – 1

Question 8

A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?

Revolt · Accepted Answer

The graph of the function is positive on (, –7).

Question 9

What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?

Revolt · Accepted Answer

As , and as , .

Question 10

A cliff diver leaps from a 100-foot cliff into the Pacific. The diver’s height above the water is modeled by the functionP(x) = –16x 2 + 10x + 100, where x is time in seconds.During which interval is the diver at least halfway down?

Revolt · Accepted Answer

2.1 < x < 2.8 seconds

Graphing Polynomial Functions — Unit test Answers

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