Whenever you have a function, think of it like a machine. When you insert, let's say, meat into a meat grinder, the grinder "transforms" the meat as its function and outputs ground beef as a result. Here's it's really no different. Our meat is -1 and our meat grinder is [tex] f(x)=x^2+1 [/tex]. Rather than making meat, though, our machine takes its input, squares it, then adds one. Now, let's insert -1 into our machine:
[tex] f(-1)=(-1)^2+1=1+1=2 [/tex]
Out function outputs 2 with an input of -1.
