Use the graph of $f(x)$ and $g(x)$ to evaluate $(f+g)(1)$

Question

Use the graphs of $f(x)$ and $g(x)$ to evaluate the following.

I've done what I think is all the work for this problem, but I'd like to make sure I'm on the right track with this. Feedback on whether or not I'm correct would be very helpful.

As far as I know, when you are adding functions (as in part a), you add the $y$-values of a point to get the $y$-value of the new function.

In the same way, when you subtract two functions you subtract the $y$-values, when you are multiplying you multiply the $y$-values, etc. Am I correct in thinking this?

Answer 1

Yes, you are thinking correctly.

• $(f+g)(1) := f(1)+g(1)$
• $(f-g)(5) := f(5)-g(5)$
• $(f/g)(-3) := f(-3)/g(-3)$
• $(fg)(5) := f(5)g(5)$

Other than this, is just looking at the drawing. After squinting my eyes a bit, I found no mistakes in your work. You're on the right track. Good studies.

Answer 2

It is correct. Because $(f+g)(x)=f(x)+g(x)$ $(fg)(x)=f(x)g(x)$ and so on.

These properties can be proven by using limit and continuity. But this requires $f(x)$ and $g(x)$ to be continuous first.