AnswersFL-1200330-Algebra 2 CRGraphing Polynomial Functions

Graphing Polynomial Functions Answers

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If a zero is , then the graph of its function only touches the x–axis at that zero.:of even multiplicity
If a zero is , then the graph of its function crosses the x–axis at that zero.:of odd multiplicity
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of odd multiplicity✔ of even multiplicity

Answers:
If a zero is , then the graph of its function only touches the x–axis at that zero.:of even multiplicity
If a zero is , then the graph of its function crosses the x–axis at that zero.:of odd multiplicity
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The zeroes of the function are -2 and 00 and 4✔ -2, 0, and 4.

A
-2 and 0
B
0 and 4
C
✔ -2, 0, and 4
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What intervals would you use to determine where the function is positive and negative?

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

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

Question illustration
A
f(x) = x (x – a)(x – b)2
B
f(x) = (x – a)(x – b)2
C
f(x) = x(x – a)³(x – b)
D
f(x) = x2(x – a) 2(x – b)2
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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:

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 ($f(x) \to \infty$ as $x \to \infty$) and rises to the right ($f(x) \to \infty$ as $x \to \infty$). 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.

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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?

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Option
Option A
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Option
Option B
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Option
Option C
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Option
Option D
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✔ of odd multiplicityof even multiplicity

A
✔ of odd multiplicity
B
of even multiplicity
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✔ NoneOneTwoThreeof the zeroes have a multiplicity of 2.

A
✔ None
B
One
C
Two
D
Three
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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.

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