Question

Which graph represents the function f(x) = x/?123 45-5-4-3-2-11--2--37N&O-5-4-3-2-1₁ 1 2 3 4-2--367321--5-4-3-2-1₁.-2--3-2345

Answer 1

Absolute value functions:

`f(x)=a\lvert{x}\rvert`

When 0
`f(x)=(1)/(3)\lvert{x}\rvert`

From the given graphs just two are compressed vertically; find the value of f when x=-3 and when x=-2 to identify the graph from those options:

`\begin{gathered} f(-3)=(1)/(3)\lvert{-3}\rvert=(1)/(3)(3)=1 \\ \\ f(-2)=(1)/(3)\lvert{-2}\rvert=(2)/(3) \end{gathered}`

Then, the graph of the given function is an absolute value graph compressed vertically and has points (-3,1) and (-2,2/3):