algebra 2 problem

Question

could someone answer this piecewise problem 

 

f(x)= piecewise [x+3 if-2<x<1

9   if x=1

-x+2 if x>1

 

I have no idea what this means or how to do it

 

 

Answer 1

Hi Debbie,

 

A piecewise function is a function that is not governed by one rule , but is governed by multiple rules.  Hence, the term "piecewise" to describe the behavior of the function in "pieces".

 

In our problem, we have three rules with each one describing a piece of the function's output (f(x) or y) based upon the function's input (x):

    1.  If the function's input value (x) is less than 1 and greater than -2 then the function's output value (y) is determined by the rule (equation):  y = x +3.

    2.  If the function's input value (x) is equal to 1 then the function's output value (y) is determined by the rule (equation):  y = 9

    3.  If the function's input value (x) is greater than 1 then the function's output value (y) is determined by the rule (equation):  y = -x + 2.

 

Below is the link to our graph of this piecewise function:

 

https://dl.dropbox.com/s/84yd5ok2ouw6pi5/Piecewise_Function.png?raw=1

 

Our graph shows the three pieces of this function where each piece is graphed in a different color as per the rule (equation) for that portion of the input range:

    1.  Blue line (y = x + 3) where -2<x<1

    2.  Red point (y = 9) where x=1

    3.  Green line (y = -x + 2) where x>1

 

Trust the above will be helpful to your understanding of what piecewise functions are and how they are graphed.

 

God bless, Jordan.