Question

What does the graph of the given function look like?

Answer 1

Have you tried graphing it?
It's easier than you think.

What does the graph of f(x) = -3 look like?

Answer 2

I have tried, but I can't figure out how. We just started piecewise functions and I'm confused

Answer 3

Ok, let's go over it step by step.

What does the graph of f(x) = -3 look like?

Answer 4

a horizontal line across y=-3

Answer 5

Great.
Like the graph below.

Answer 6

We are told that f(x) = -3 only for x < -5.
So now we will redo the graph above but for x only from negative infinity to -5.

Answer 7

Now, for \(-5 \le x \le 15\), f(x) = x + 2.
As you can see, f(x) = x + 2 is a linear equation whose graph is a straight line.
If we find f(-5), and f(15), we can plot those the two points (-5, f(-5)) and (15, f(15)), and the line will connect those two points.

Answer 8

Once again, for the domain part \(-5 \le x \le 15\), f(x) = x + 2,
so
f(-5) = -5 + 2
f(-5) = -3
and
f(15) = 15 + 2
f(15) = 17

Now we have two points for the endpoints of the segment of the middle portion of our piecewise function. The points are: (-5, -3) and (5, 17). Now we plot them.