Polynomial Functions

Polynomial Functions

Analyzing graphs

This is the graph of

 $f\left(x\right)=x\left(x+3\right)\left(x-1\right)$  

What is its domain?

 $f\left(x\right)=x\left(x+3\right)\left(x-1\right)$  

What is its range?

 $f\left(x\right)=x\left(x+3\right)\left(x-1\right)$  

How many "turns" does the graph have?

 $f\left(x\right)=x\left(x+3\right)\left(x-1\right)$  

What is the behavior of y-values before the first turn?  (From left to right)

 $f\left(x\right)=x\left(x+3\right)\left(x-1\right)$  

What is the behavior of y-values in between the two turns?  (From left to right)

 $f\left(x\right)=x\left(x+3\right)\left(x-1\right)$  

What is the behavior of y-values after the last turn?  (From left to right)

 $f\left(x\right)=x\left(x+3\right)\left(x-1\right)$  

These "turns" are called "relative extrema"

Relative maximum or minimum

We can use their x-values to define domains of increase or decrease

We also call those "intervals"