Graphing Polynomial Functions Assignment

The zeroes of the function are _________ ______of the zeroes have a multiplicity of 2. What intervals would you use to determine where the function is positive and negative?

-2, 0, and 4 None B

Choose all of the zeroes of f(x).

-3 with multiplicity 1 3 with multiplicity 1 0 with multiplicity 3 crosses

Consider the function f(x) = (x − 3)2(x + 2)2(x − 1).

1, 2

Let a and b be real numbers, where a =/= b =/= 0. Which of the following functions could represent the graph on the right?

A

A polynomial function has a root of 0 with multiplicity 1, and a root of 2 with multiplicity 4. If the function has a negative leading coefficient, and is of odd degree, which of the following are true?

A,B,C

Which of the following could represent the graph of f(x) = x4 + x3 - 8x2 - 12x?

B

What is the end behavior of the graph of f(x) = x5 - 8x4 + 16x3?

B 4 0

If a zero is ________, then the graph of its function only touches the x-axis at that zero. If a zero is ________, then the graph of its function crosses the x-axis at that zero.

Even, Odd

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 infinity, f(x) goes to [___] infinity.

Negative, Positive

Check all the statement(s) that are true about the polynomial function graphed.

Options B, C, F, G

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.

The degree of the function is odd and the leading coefficient is positive - so the function goes to negative infinity as x goes to negative infinity and to positive infinity as x goes to positive infinity. The zeroes are -4, 0, and 2, all with multiplicity 1. The function is negative from negative infinity to -4 and from 0 to 2. The function is positive from -4 to 0 and from 2 to infinity.