End Behavior

Lesson 8 End Behavior Part 1

Multiple Choice

Match the polynomial with its end behavior.

$$f\left(x\right)=2x^3+3x^4+x^2-1$$  

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the positive direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the negative direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the negative direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the negative direction.

Multiple Choice

Match the polynomial with its end behavior.

$$f\left(x\right)=1-3x+x^2$$  

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the positive direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the negative direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the negative direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the negative direction.

Multiple Choice

Match the polynomial with its end behavior.

$$f\left(x\right)=9+x^4$$  

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the positive direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the negative direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the negative direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the negative direction.

Multiple Choice

Match the polynomial with its end behavior.

$$f\left(x\right)=9-x^4$$  

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the positive direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the negative direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the negative direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the negative direction.

Multiple Choice

Match the polynomial with its end behavior.

$$f\left(x\right)=2x+5$$  

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the positive direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the negative direction.

• As x gets larger and larger in the positive direction, f(x) gets larger and larger in the negative direction. As x gets larger and larger in the negative direction, f(x) gets larger and larger in the positive direction.

• As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the negative direction.

Multiple Choice

Which polynomial function gets larger and larger in the negative direction as x gets larger and larger in the negative direction?

• $$f\left(x\right)=5x^2-2x+1$$

• $$f\left(x\right)=6x^3+4x^2-15x+32$$

• $$f\left(x\right)=7x^4-2x^3+3x^2+8x-10$$

• $$f\left(x\right)=8x^6+1$$

Multiple Choice

The graph of a polynomial function f is shown. Which statement about the polynomial is true?

• The degree of the polynomial is even.

• The degree of the polynomial is odd.

• The constant term of the polynomial is even.

• The constant term of the polynomial is odd.

Open Ended

Multiple Choice

Rewrite the polynomial in standard form.

$$f(x)=(3x+1)(x+2)(x−3)$$  

• $$f\left(x\right)=3x^3-2x^2-19x-6$$  

• $$f\left(x\right)=3x^3+2x^2+19x-6$$  

• $$f\left(x\right)=-3x^3-2x^2-19x-6$$  

• $$f\left(x\right)=3x^3-2x^2-19x+6$$  

Multiple Choice

Rewrite the polynomial in standard form.

$$f(x)=-2(3x+1)(x+2)(x−3)$$  

• $$f\left(x\right)=6x^3-2x^2-19x-6$$  

• $$f\left(x\right)=6x^3+2x^2+19x-6$$  

• $$f\left(x\right)=-6x^3-4x^2-38x+12$$  

• $$f\left(x\right)=-6x^3+4x^2+38x+12$$  

Open Ended

Kiran wrote f(x)=(x−3)(x−7) as an example of a function whose graph has x-intercepts at x=-3,-7. What was his mistake?

Open Ended

A polynomial function, f(x), has x-intercepts at (-6,0) and (2,0). What is one possible factor of f(x)?