How are the graphs $f (x) = | x |$ $f(x)=absx$ and $g (x) = - 9 | x + 1 |$ $g(x)=-9abs(x+1)$ related?

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Answer 1 · 2018-07-03T22:03:07

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Given: $f (x) = | x |$ $f(x) = |x|$ and $g (x) = - 9 | x + 1 |$ $g(x) = -9|x+1|$

$f (x) = | x |$ $f(x) = |x|$ is the parent function.
Graph of $f (x) = | x |$ $f(x) = |x|$ :

graph{|x| [-10, 10, -5, 5]}

Graph of $g (x) = - 9 | x + 1 |$ $g(x) = -9|x+1|$ :

graph{-9|x+1| [-10, 10, -5, 5]}

You can see that the graph is reflected about the $x$ $x$ axis,

shifted horizontally left by $1$ $1$ and stretched vertically by a factor of $9$ $9$ .

How are the graphs f(x)=|x|f(x)=absx and g(x)=−9|x+1|g(x)=-9abs(x+1) related?