Question

Which graph represents the function f(x) = 1/3|x|?

Answer 1

Answer:

The correct option is 4.

Step-by-step explanation:

The given function is,

$f(x)=\frac{1}{3}|x|$

It is a modulus function and its parent function is,

$g(x)=|x|$

In a function,

$f(x)=k|x|$

If k>1, then the graph of g(x) stretch vertically and if k<1 then the graph of g(x) compressed vertically.

Since k is $\frac{1}{3}$, therefore the shoes the vertical compression.

put x=0 in the given function.

$f(0)=\frac{1}{3}|0|=0$

Put x=3.

$f(3)=\frac{1}{3}|3|=1$

Therefore the graph passing through (0,0) and (3,1).

Thus fourth option is correct.

Answer 2

Seeing from the graph I've provided above, the correct answer would be D, the last one.