How do you graph y= |x+1|y=|x+1|?

1 Answer
Jul 26, 2018

graph{y=|x+1| [-8.08, 7.68, -1.54, 6.336]}
Shift y=|x|y=|x|
or
Sketch two linear functions (lines)

Explanation:

The easiest way to do this is to just shift the graph of y=|x|y=|x| one unit to the left.

We can see this a lot more clearly if we set f(x) = |x|f(x)=|x|, so f(x+1)=|x+1|f(x+1)=|x+1|, indicating a one unit shift to the left.

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An alternative way of graphing y=|x+1|y=|x+1| is to think of it as two linear functions. The function depends on whether x+1x+1 is negative or positive.

We know when x >= -1x1, y = x+1y=x+1

and when x < -1x<1, y = -x-1y=x1

We can rewrite this as a piecewise function:

f(x) = { (x>= -1 ", " x+1), (x<-1 ", " -x-1) :}

We essentially sketch the graph of y=x+1 on the right of x=-1

and we sketch the graph of y=-x-1 on the left of x=-1.