Sketching Modulus functions. Any Tips?

[cameron_15]

So I'm doing revision and I came across a question asking me to draw the graph of a function with modulus x values and normal x values.

I saw it and had no real idea what to do, so I just put in an x value and started plotting points. It was a linear function so it was pretty easy and the write answer came about without pain. However, what if they aren't as nice? do you guys have any tips on how to go about them? or is it simply a matter of plotting a few points to find the general shape of the graph?

For reference, the function was f(x)=|2x|+x

[TrueTears]

split into hybrid equation, draw separate functions on same axis.

these should be the general method to draw hybrid graphs, the 2 'exceptions' are only special cases of this.

[brightsky]

General rule for sketching modulus graphs are to sketch the graph inside the absolute value and then flip anything that is below the y-axis.

For example if you have something like: , then you first sketch and then flip any part of the graph that's below the y-axis about the y-axis.

For your question: , is the same as

If , then .

If , then

If , then

Sketch the two graphs on the same set of axis, and observing that for any x, we cut off any part of the graph that is under the y-axis.

[Martoman]

^^ what brightsky said.

For normal graphs like y = |x+1| its an upside-down roof