Evaluating Functions

Evaluating Functions

Feb 1

Function Notation

f(x)

We call this "f of x"

f is the function name and x is the input

f(x) is the output

Input: what gets plugged in

Output: the answer for the given input

Example:

 $f\left(x\right)=x^2-9x+2$  

Evaluate: f(4)
plug in 4 everywhere there is an x:
 $f\left(4\right)=4^2-9\left(4\right)+2$  
evaluate:
 $f\left(4\right)=16-36+2$  
solve:
 $f\left(4\right)=-18$  

Multiple Choice

 $f\left(x\right)=x^2-9x+2$  
Evaluate:  $f\left(-2\right)$  

•  $f\left(-2\right)=24$  

•  $f\left(-2\right)=-20$  

•  $f\left(-2\right)=16$  

•  $f\left(-2\right)=-12$  

 $f\left(x\right)=x^2-9x+2$  
Evaluate:  $f\left(-2\right)$  

• Plus in -2 for x in function:  $f\left(-2\right)=\left(-2\right)^2-9\left(-2\right)+2$  

• Evaluate:  $\left(-2\right)^2=4,\ \ -9\left(-2\right)=18$  

• solve:  $f\left(-2\right)=4+18+2=24$  

•  $f\left(-2\right)=24$  

The function name can change, but your process doesn't

 $g\left(x\right)=-7x+9$  
This function is g of x, instead of f of x. But that doesn't matter.

 $g\left(x\right)=-7x+9$  

Evaluate: g(-1)
Plug in -1 for all values of x
 $g\left(-1\right)=-7\left(-1\right)+9$  
evaluate
 $g\left(-1\right)=7+9$  
solve
 $g\left(-1\right)=16$  

Open Ended

 $g\left(x\right)=-7+9$  

Evaluate: g(5)

Open Ended

 $g\left(x\right)=-7+9$  
evaluate: g(-3)

Open Ended

 $h\left(x\right)=x^2-4x$  
Evaluate: h(-3)

Open Ended

 $h\left(x\right)=x^2-4x$  
evaluate: h(3)

Open Ended

 $h\left(x\right)=x^2-4x$  
evaluate: h(-5)