Lesson 10

Multiplicity

View Student Lesson

Problem 1

Draw a rough sketch of the graph of \(g(x)=(x-3)(x+1)(7x-2)\).

Solution

For access, consult one of our IM Certified Partners.

Problem 2

Draw a rough sketch of the graph of \(f(x)=(x+1)^2(x-4)\).

Solution

For access, consult one of our IM Certified Partners.

Problem 3

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

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

Solution

For access, consult one of our IM Certified Partners.

Problem 4

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?​​

A:

10

B:

\(5x^3\)

C:

\(5x^7\)

D:

\(x^{10}\)

Solution

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 3.)

Problem 5

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

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

Solution

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 6.)

Problem 6

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

Solution

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 8.)

Problem 7

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

polynomial function graphed. x intercepts = about -2 point 6 and 2 point 6. y intercept = 3. f of f decreases as x increases. 
A:

The degree of the polynomial is even.

B:

The degree of the polynomial is odd.

C:

The leading coefficient is positive.

D:

The leading coefficient is negative.

E:

The constant term of the polynomial is positive.

F:

The constant term of the polynomial is negative.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 9.)