Question

Can someone tell me what I am doing wrong? Do I need to graph this to get the right answers?

Problem:
Find the requested value.
f(3) for f(x)
3x+1, if x<1=3(3)+1=10
3x, if 3<=x<=8=3(3)=9
3-5x, if x>8=3-5(3)=-12

Answer 1

Only the middle one counts as I understand your question.
x is not less than one. It is three
When x is 3, then 3<= x
x is not more than eight,. It is three.

so for x = 3 , f(x) = 3 x = 9

Answer 2

But the reason I am having trouble is because the middle one does not work.

The first part works, but the second part does not.
3<=x<=8=3(3)=9
8=3(3)=9 (?)

Answer 3

That just means that between x = 3 and x = 8 (including 3 and 8)
You can use
y = 3 x
if x were 4, you could say y = 3*4 = 12
BUT
if x is 9 , you are not allowed to use this relation and have to use some other one.
In this particular case, you would use
y = 3 - 5x
if x were 9, which is greater than 8

Answer 4

Thank-you for explaining it.