Question

Find the following values of the functionf(3) =-30 +473 +40<-44 < x < 02 > 0f(-7) =f(-4) =f(-2) =f(2)=

Answer 1

So, as you can see, the function given is drawn up there.

We're asked to find the value of:

$f(-7)$

This can be found if we evaluate the function f(x) at the point x=-7. Notice that -7 is a number clearly less than -4, so we're going to replace x=-7 in the part of the function where x≤-4. This is

$\begin{gathered} f(-7)=-3(-7)+4 \\ f(-7)=21+4 \\ f(-7)=25 \end{gathered}$

If we want to find f(-4), we're going to replace x=-4 in the first part of the function. Since this part is less or equal than x=-4, we could write:

$\begin{gathered} f(-4)=-3(-4)+4 \\ f(-4)=12+4 \\ f(-4)=16 \end{gathered}$

Now, to find f(-2), remember that the function is 7 for all the values between x = -4 and x = 0, and -2 is actually a value between these, so:

$f(-2)=7$

Finally, to find f(2) we could replace x=2 in the third part of the function since x=2 is greater than zero. This is:

$\begin{gathered} f(2)=3+4(2) \\ f(2)=3+8 \\ f(2)=11 \end{gathered}$