Absolute modulus graphs (1 Viewer)

[skillz]

Hi guys. I'm doing the VCE but I thought i'd post here cause this forum is more popular.


I don't understand how to draw the function y=|x+2|

i know that for y=|x|, it's made up of two linears, y=x and y=-x with a range of [0,infinte]

Is there anything else i should know about?

 

[Riviet]

Okay, for your example, y=|x+2|, consider x>-2. Any x-values in this domain will be zero or positive, and taking the absolute value does nothing to a positive number (y-value) so you graph this part on the number plane the same way you would for y=x+2 with x>0.
Now consider x<-2, observe that ALL values of x in this domain will produce a negative value of y, so the diagonal line would continue along to the bottom left. But, you are taking the absolute value of this negative number, which changes it to it's corresponding positive, e.g y=|-5+2|=|-3|=3. This will occur for any x value in the domain x<-2 that you substitute into the original equation. So therefore we can say that the part of y=|x+2| for x<-2 is reflected in the x-axis which means the negative y-values become positive, therefore resulting in a V shaped graph. where the angle at the inside the V is 90 degrees. Hope that helps.

P.S If you have any more problems, feel free to ask.