Thread: Piecewise Defined Function

Evaluate the following piecewise defined function.

f(x) = {x^2 - 1...if x < 2
.........{2 - x.......if x>or=to2

Originally Posted by magentarita

Evaluate the following piecewise defined function.

f(x) = {x^2 - 1...if x < 2
.........{2 - x.......if x>or=to2

I'm not sure what " x>or=to2 " is? Also, where do you want to evaluate this function?

Originally Posted by danny arrigo

I'm not sure what " x>or=to2 " is?

She probably meant $\displaystyle x \geq 2$

Also, where do you want to evaluate this function?

We're on the same boat.

Originally Posted by Chop Suey

She probably meant $\displaystyle x \geq 2$


We're on the same boat.

Of course, I should of just look at it "x > or = 2". That's

Originally Posted by magentarita

Evaluate the following piecewise defined function.

f(x) = {x^2 - 1...if x < 2
.........{2 - x.......if x>or=to2

I guess you just mean to graph the two functions with their respective restricted domains.

$\displaystyle f(x)=\left\{ \begin{array}{rcl}x^2-1 & \mbox{if} & x<2 \\ 2-x & \mbox{if} & x \geq 2 \end{array} \right.$

Make a table for each function and then graph them. (if not using a graphing calculator)

Code:

x | f(x)=x^2 -1
------------------
2 | 3 (not included in graph since x < 2)
1 | 0
0 | -1
-1| 0
-2| 3

Code:

x | f(x)=2 - x
------------------
2 | 0 (included in graph since x >= 2)
3 | -1
4 | -2
5 | -3

See my crude graph.

Originally Posted by masters

I guess you just mean to graph the two functions with their respective restricted domains.

$\displaystyle f(x)=\left\{ \begin{array}{rcl}x^2-1 & \mbox{if} & x<2 \\ 2-x & \mbox{if} & x \geq 2 \end{array} \right.$

Make a table for each function and then graph them. (if not using a graphing calculator)

Code:

 
x | f(x)=x^2 -1
------------------
2 | 3 (not included in graph since x < 2)
1 | 0
0 | -1
-1| 0
-2| 3

Code:

x | f(x)=2 - x
------------------
2 | 0 (included in graph since x >= 2)
3 | -1
4 | -2
5 | -3

See my crude graph.

Nicely done and great graph!