Algebra /pre calc question

Question

Gaph the piecewise defined function

y=f(x)={x+7,if x<0

7,if x is less than or equal to 0

Answer 1

Piecewise functions are a bit like puzzles. They tell you what graphs make up the pieces of the larger picture, and what sections of the graphs need to be drawn (instead of drawing the entire line or curve).

In your function, you have two pieces: y = x + 7 and y = 7. First think about what these graphs would look like on their own. Are they diagonal lines? Horizontal or vertical? Curves? Try drawing them out on two separate graphs, using a table to make a set of points to plot, if needed.

Then, take a look at what sections of each graph need to be shown in your final answer. For y = x+7, you are told you only want to draw the part of the graph where the x values are less than zero (x < 0). This is the section of the graph to the left of the y-axis, all the way up until the y-axis itself. For y = 7, you only want to draw the part of the graph where the x values are greater than or equal to zero (x >= 0). This is the section of the graph to the right of the y-axis, starting on the y-axis itself.

Once you know what your two pieces are, draw them on the same coordinate plane. You'll need to be a little careful about whether or not the two pieces connect, sometimes they do and sometimes they don't. When the piecewise graph is done you should see two distinct pieces - one that looks like a chunk of the y = x +7 graph and one that looks like a chunk of the y = 7 graph and they two graphs should not cross.