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
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
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 (?)
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
Thank-you for explaining it.
To find the value of f(3) for the given function, you can follow these steps:
1. Look at the three different conditions defined for the function f(x).
- If x < 1, the function is given by f(x) = 3x + 1.
- If 3 ≤ x ≤ 8, the function is given by f(x) = 3x.
- If x > 8, the function is given by f(x) = 3 - 5x.
2. Since you are trying to find f(3), you need to determine which condition applies to this value.
3. In this case, 3 does not satisfy the condition x < 1 or x > 8, so the corresponding equation you need to use is f(x) = 3x.
4. Substitute x = 3 into the equation f(x) = 3x:
f(3) = 3(3) = 9.
Therefore, the value of f(3) for the given function is 9.
Graphing the function could also help you visualize and understand its behavior, but it is not required to find the value of f(3) in this case.