Graphing Polynomial Functions

Question 1

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.

Revolt · Accepted Answer

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

Question 2

✔ NoneOneTwoThreeof the zeroes have a multiplicity of 2.

Revolt · Accepted Answer

None

Question 3

What intervals would you use to determine where the function is positive and negative?

Revolt · Accepted Answer

Answer image: https://media.edgenuity.com/EVresources/3111-06-09-25-06-task/mc001-2.jpg

Question 4

The zeroes of the function are .

Revolt · Accepted Answer

-2, 0, and 4

Question 5

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

Revolt · Accepted Answer

Answer image: https://media.edgenuity.com/EVresources/3111-06-09-25-07-task/mc001-2.jpg

Question 6

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 7

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

To sketch $f(x) x^3 2x^2 8x$, first determine the end behavior: since the degree is odd (3) and the leading coefficient is positive (1), the graph falls to the left ($f(x) 	o \infty$ as $x 	o \infty$) and rises to the right ($f(x) 	o \infty$ as $x 	o \infty$). Next, find the zeros by factoring: $x(x^2 2x 8) x(x 4)(x 2) 0$, giving zeros at $x 4, 0,$ and $2$, each with multiplicity 1. Finally, test the intervals: the function is negative on $(\infty, 4)$ and $(0, 2)$, and positive on $(4, 0)$ and $(2, \infty)$. Plot these intercepts and draw a smooth curve following these characteristics.

Question 8

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?

Revolt · Accepted Answer

Answer image: //media.edgenuity.com/EVresources/3111-06-09-25-10-task/mr001-1.jpg; Answer image: //media.edgenuity.com/EVresources/3111-06-09-25-10-task/mr001-2.jpg; Answer image: //media.edgenuity.com/EVresources/3111-06-09-25-10-task/mr001-3.jpg

Question 9

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.

Revolt · Accepted Answer

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

Question 10

Choose all of the zeroes of f(x).

Revolt · Accepted Answer

–3 with multiplicity 1; 3 with multiplicity 1; 0 with multiplicity 3

Graphing Polynomial Functions Answers

More from this Course

TRY EDGENUITY HACKS