SOLUTION: for each piecewise function, find the specified function values f(x)= 3 for x <= -2 (1/2)x + 6 for x > -2 f(-5),f(-2),f(0), f(2) <= means less th

Algebra ->  Functions -> SOLUTION: for each piecewise function, find the specified function values f(x)= 3 for x <= -2 (1/2)x + 6 for x > -2 f(-5),f(-2),f(0), f(2) <= means less th      Log On


   



Question 633336: for each piecewise function, find the specified function values
f(x)= 3 for x <= -2
(1/2)x + 6 for x > -2
f(-5),f(-2),f(0), f(2)
<= means less than or equal to. i wasnt sure how to do the sign
for the second equation i (think) that i make for example -5 for x. not sure on first one
thanks

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Good job with the definition of the function. The <= , and the (1/2)x make me pretty sure that I understand what you mean.
As I understand, the function is defined in pieces:
f%28x%29=3 for x%3C=-2 and
f%28x%29=%281%2F2%29x%2B6 for x%3E2
and you need to calculate the value of f%28x%29
for x=-5, x=-2, x=0 and x=2.

x=-5, and x=-2 are in the first part of the domain,
the part where x%3C=-2.
In that part, f%28x%29=3, so
highlight%28f%28-5%29=3%29 and highlight%28f%28-2%29=3%29

x=0, and x=2 are in the other part of the domain,
the part where x%3E-2.
In that part, f%28x%29=%281%2F2%29x%2B6, so we enter the x value into f%28x%29=%281%2F2%29x%2B6 to calculate the f%28x%29 values:
For x=0, f%280%29=%281%2F2%29%2A0%2B6=0%2B6=6 so highlight%28f%280%29=6%29
For x=2, f%282%29=%281%2F2%29%2A2%2B6=1%2B6=7 so highlight%28f%282%29=7%29

The problem does not ask for a graph, but I like to draw these pictures.
The graph of that piecewise function looks like this:
I drew the function in blue and put green circles around the 4 points (x,f(x)) that we calculated.