AnswersFL-1200330-Algebra 2 CRGraphing Polynomial Functions

Graphing Polynomial Functions Answers

3 verified answers2 views
1
Free Preview

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.

Answer:

Factor f(x) = x(x + 4)(x - 2). The zeroes are -4, 0, and 2, each with multiplicity 1, so the graph crosses the x-axis at each one. Since the function has odd degree and a positive leading coefficient, its left end falls toward negative infinity and its right end rises toward positive infinity. The function is negative on (-infinity, -4) and (0, 2), and positive on (-4, 0) and (2, infinity). Use these points and signs to draw a smooth cubic curve.

2
Free Preview

Did your explanation include the following?

A
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.
B
The zeroes are –4, 0, and 2, all with multiplicity 1.
C
The function is negative from negative infinity to –4 and from 0 to 2.
D
The function is positive from –4 to 0 and from 2 to infinity.
3

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
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

Did you find these answers helpful?

More from this Course

Assignment
20 verified answers

Assignment

Assignment
20 verified answers

Graphing Polynomial Functions

Assignment
22 verified answers

Graphing Polynomial Functions