OpenStudy (anonymous):

What does the graph of the given function look like?

4 years ago
OpenStudy (anonymous):
4 years ago

OpenStudy (mathstudent55):

Have you tried graphing it? It's easier than you think. What does the graph of f(x) = -3 look like?

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (mathstudent55):

Ok, let's go over it step by step. What does the graph of f(x) = -3 look like?

4 years ago
OpenStudy (anonymous):

a horizontal line across y=-3

4 years ago
OpenStudy (mathstudent55):

Great. Like the graph below. |dw:1377012791805:dw|

4 years ago
OpenStudy (mathstudent55):

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.

4 years ago
OpenStudy (mathstudent55):

|dw:1377012984158:dw|

4 years ago
OpenStudy (mathstudent55):

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.

4 years ago
OpenStudy (mathstudent55):

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.

4 years ago
OpenStudy (mathstudent55):

|dw:1377013321399:dw|

4 years ago