There is no absolute value function, when graphed, will be wider than the graph of the parent function f(x) = |x|
What is an absolute value function?
An absolute value function is a function such that,
[tex]|x|=\left \{ {{x}~~ (x~\geq~0) \atop {-x}~~(x~ < ~0)} \right.[/tex]
For given example,
we have been given a parent function f(x) = |x|
We need to find the absolute value function, when graphed, will be wider than the graph of the parent function.
Consider the graph of all absolute value functions.
The graph of f(x) = |x| + 3 is represented blue color.
The graph of f(x) = |x − 6| is represented green color.
The graph of f(x) = |x| is represented red color.
the graph of f(x) = 9|x| is represented violet color.
From this graph we can observe that,
f(x) = |x| + 3 is as wise as the parent absolute value function f(x) = |x| translated up by 3 units.
Similarly, the function f(x) = |x - 6| is as wise as the parent absolute value function f(x) = |x| translated right by 6 units.
This means, there is no absolute value function, when graphed, will be wider than the graph of the parent function f(x) = |x|
Learn more about absolute value function here:
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