Lesson 9

End Behavior (Part 2)

The practice problem answers are available at one of our IM Certified Partners

Problem 1

Match the polynomial with its end behavior.

Problem 2

State the degree and end behavior of \(f(x)=\text-x^3+5x^2+6x+1\). Explain or show your reasoning.

Problem 3

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

graph of a polynomial function. x intercepts of -2, 0 point 5, and 3. y intercept = 6. f of x increases as x increases in the positive direction.
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.

Problem 4

Write the sum of \(5x^2 + 2x - 10\) and \(2x^2 + 6\) as a polynomial in standard form.

(From Algebra2, Unit 2, Lesson 4.)

Problem 5

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

(From Algebra2, Unit 2, Lesson 8.)

Problem 6

Select all the polynomial functions whose graphs have \(x\)-intercepts at \(x=4,\text-\frac14,\text-2\).

A:

$(x+4)(4x-1)(x-2)$

B:

$(x-4)(4x+1)(x+2)$

C:

$(x-4)(4x-1)(x-2)$

D:

$(x+4)(4x+1)(x+2)$

E:

$(2x+4)(4x - 1)(x-2)$

F:

$(4x-16)(4x + 1)(x + 2)$

(From Algebra2, Unit 2, Lesson 7.)