Review of Graphs of Polynomial Functions

Review of Graphs of Polynomial Functions

Keep track of your answers so you can provide them when needed

Part 1: Review of end behavior and factoring

When in doubt... graph it!

You are given the function

 $f\left(x\right)=x^3-4x^2+3x-12$  

• What is the parity of the degree?  (odd or even?)

• What sign is the lead coefficient? (positive or negative?)

Multiple Choice

Given the function

 $f\left(x\right)=x^3-4x^2+3x-12$  What is its end behavior?

• Left, down; right, down

• Left, up; right, up

• Left, down; right, up

• Left, up; right, down

You are given the function

 $f\left(x\right)=x^3-4x^2+3x-12$  

• What is its factored form?

• Take time to work on it on your own first.

Multiple Choice

Given the function

 $f\left(x\right)=x^3-4x^2+3x-12$  What is its factored form?

• It cannot be factored

•  $\left(x^2-4\right)\left(x+3\right)$  
  

•  $\left(x^2-3\right)\left(x+4\right)$  
  

•  $\left(x^2+3\right)\left(x-4\right)$ 

Part 2: Review of zeros, multiplicity, and behavior at x-intercepts.

Pay close attention to exponents!

You are given the function

 $f\left(x\right)=-x\left(x+2\right)\left(x-5\right)^2$  

• What are the zeros?

• What is their multiplicity? (odd or even?)

• Write it down on your paper first.

Multiple Choice

Given the function

 $f\left(x\right)=-x\left(x+2\right)\left(x-5\right)^2$  What are the zeros?  What is their multiplicity?

• 0, even; -2, odd; 5, odd

• -2, odd; 5, even

• 0, odd; -2, odd; 5, even

• 0, odd; -2, even; 5, odd

You are given the function

 $f\left(x\right)=-x\left(x+2\right)\left(x-5\right)^2$  

• Where are the x-intercepts?

• What is the behavior of the graph at each x-intercept?

Multiple Choice

Given the function

 $f\left(x\right)=-x\left(x+2\right)\left(x-5\right)^2$  Where are the x-intercepts?  What is the behavior of the graph at each x-intercept?

• (0,0); (-2,0); (5,0):  Cross, bounce, cross

• (0,0); (-2,0); (5,0):  Bounce, bounce, cross
  

• (0,0); (-2,0); (5,0):  Cross, bounce, bounce
  

• (0,0); (-2,0); (5,0):  Cross, cross, bounce
  

Check your work!

This is the graph of

 $f\left(x\right)=-x\left(x+2\right)\left(x-5\right)^2$  

Part 3: Review of relative extrema and domains of increase or decrease

When in doubt... graph it!

How many relative extrema does this graph have?  (Think: "How many times does it turn?")

This is the graph of

 $f\left(x\right)=-x\left(x+2\right)\left(x-5\right)^2$  

Multiple Choice

Given the function

 $f\left(x\right)=-x\left(x+2\right)\left(x-5\right)^2$  How many relative extrema are there?  What type?

• Three:  two relative minimums and one relative maximum

• Three:  two relative maximums and one relative minimum
  

• Two:  one relative maximum and one relative minimum

• One:  relative minimum
  

What are the domains of increase and decrease, from left to right?  

This is the graph of

 $f\left(x\right)=-x\left(x+2\right)\left(x-5\right)^2$  

Multiple Choice

Given the function

The Domains of increase are  $\left(-\infty,-1.158\right]\ U\ \left[2.158,\ 5\right]$  

• True

• False
  

Multiple Choice

Given the function

The Domains of decrease are  $\left[-1.158,\ 2.158\right]\ U\ \left[5,\ \infty\right)$  

• True

• False