1. ## Piecewise Defined Function

Evaluate the following piecewise defined function.

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

2. 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?

3. 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.

4. 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

5. 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.

6. ## nice work...

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!