How are the graphs $f (x) = | x |$ $f(x)=absx$ and $g (x) = | x + 4 |$ $g(x)=abs(x+4)$ related?

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Answer 1 · 2016-11-05T19:22:55

The only difference between the graphs of $f (x)$ $f(x)$ and $g (x)$ $g(x)$ is that $g (x)$ $g(x)$ is $f (x)$ $f(x)$ translated left 4 units.

$f (x) = | x |$ $f(x) = |x|$ is graphed below
graph{|x| [-9.75, 10.25, -2.08, 7.92]}

$g (x) = | x + 4 |$ $g(x) = |x+4|$ is graphed below
graph{|x+4| [-9.75, 10.25, -2.08, 7.92]}

As you can see, they are the same graph, but $g (x)$ $g(x)$ is $f (x)$ $f(x)$ shifted 4 units left.

How are the graphs f(x)=|x|f(x)=absx and g(x)=|x+4|g(x)=abs(x+4) related?