Unit 2, Lesson 10

Multiplicity

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Integrated Math 3

Practice

Problem 1

Sketch a graph of the function $g$ defined by $g(x)=(x-3)(x+1)(7x-2)$.

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Problem 2

Sketch a graph of the function $f$ defined by $f(x)=(x+1)^2(x-4)$.

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Problem 3

Technology required. Predict the end behavior of each polynomial function, then check your prediction using technology.

$A(x) = (x + 3)(x - 4)(3x - 7)(4x - 3)$
$B(x) = (3 - x)^2(6 - x)$
$C(x) = \text-(4 - 3x)(x^4)$
$D(x) = (6 - x)^6$

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Problem 4

ForLesson 3: Introducing Polynomials

Which term can be added to the polynomial expression $5x^{7}-6x^{6}+4x^4-4x^2$ to make it into a 10th degree polynomial?

10
$5x^3$
$5x^7$
$x^{10}$

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Problem 5

ForLesson 6: Different Forms

$f(x)=(x+1)(x-6)$ and $g(x)=2(x+1)(x-6)$. The graphs of each are shown.

<p>Coordinate plane, x, negative 5 to 9 by 1, y, negative 25 to 10 by 5. Parabola, solid, through negative 1 comma 0 & 6 comma 0, minimum at 2 point 5 comma negative 12 point 2 5. Dotted parabola, same x-intercepts, minimum at 2 point 5 comma negative 24 point 5.</p>

Which graph represents which polynomial function? Explain how you know.

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Problem 6

ForLesson 8: End Behavior (Part 1)

State the degree and end behavior of $f(x)=8x^3+2x^4-5x^2+9$. Explain or show your reasoning.

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Problem 7

ForLesson 9: End Behavior (Part 2)

The graph of a polynomial function $f$ is shown. Select all the true statements about the polynomial.

<p>polynomial function graphed. x intercepts = about -2 point 6 and 2 point 6. y intercept = 3. f of f decreases as x increases. </p>

The degree of the polynomial is even.
The degree of the polynomial is odd.
The leading coefficient is positive.
The leading coefficient is negative.
The constant term of the polynomial is positive.
The constant term of the polynomial is negative.

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Multiplicity

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Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Lesson 10 Resources