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How do you graph #y = abs(x+6)#?

Answer 1

See explanation

Let's start by looking at its parent function: #y=absx#
graph{|x| [-9.97, 10.03, -0.6, 9.4]}
Now looking at #y=abs(x+6)# and the given transformation rules below...

...we can see the we must shift the entire graph #6# units to the left

To do that, we take each point on the graph and subtract #6# from the #x# value.

For example:

The point #(0,0)# shifted #6# units to the left is:

#(0color(blue)(-6),0)=>(-6,0)#

Once we do that we'll get the following graph...
graph{|x+6| [-14.34, 5.66, -0.88, 9.12]}
...which is the graph of #y=abs(x+6)#

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Answer 2

Jace Anderson

To graph ( y = \lvert x + 6 \rvert ), you would start by plotting the vertex point at (-6,0) and then plot the points symmetrically on both sides of the vertex. For values of x less than -6, the graph would be a reflection of the positive side of the x-axis.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.