How would you graph this function?

Question

How would you go about graphing something like this:

h(x)= x+3 if x<3

{3-x if 1<x<3

3x if x>3

*all three of those are included in h(x)*

what do all of these things mean, and how do you tell if X is greater than or less than those numbers?

Answer 1

This is a piecewise function...meaning that the function is cut into little pieces (in this case, three pieces). I assume that it is:

h(x)= x+3 if x&lt;1

{3-x if 1&lt;x&lt;3

3x if x&gt;3

To graph it, do it one equation at a time.

Graph the line (lightly, in pencil, because you are going to erase stuff in a bit) y = x + 3 first. Draw a dot at the point (0, 3). From there, go up one and right one (because the slope is 1) and draw another dot. Connect the dots using a ruler. Now, go to the spot where x = 1 (the point (1, 4)) and draw an open circle (since it is &lt; and not &lt;=) at that spot. Erase the line to the right of the dot.

Next, graph the line (again, lightly) y = 3 - x. Draw a dot at the point (0, 3). From there, go down one and right one (because the slope is -1) and draw another dot. Connect the dots using a ruler. Now, go to the spot where x = 1 (the point (1, 2)) and draw an open circle at that spot. Go to the spot where x = 3 (the point (3, 0)) and draw another open circle. Erase this line to the left of the first circle and to the right of the second circle.

Finally, graph the line y = 3x. Draw a dot at the point (0, 0). From there, go up three and right one (because the slope is 3) and draw another dot. Connect the dots using a ruler. Now, go to the spot where x = 3 (the point (3, 9)) and draw an open circle at that spot. Erase this line to the left of the circle.

That&#039;s it...hope it helps!

Edit:

&quot;They&quot; have to tell you what x is...this tells you which equation to use depending on what they say. For instance, if you are told to evaluate the function at x = 4, then use the last part (since 4 &gt; 3), but if they tell you to evaluate x = 2, then use the second part (since 2 is between 1 and 3).