Question

Suppose f(x) = x^2 and

Answer 1

Given:

The two functions are:

$f(x)=x^2$

$g(x)=\left(\dfrac{1}{3}x\right)^2$

To find:

The statement that best compares the graph of g(x) with the graph of f(x).

Solution:

The horizontal stretch is defined as:

$g(x)=f(kx)$            ...(i)

If $0$, the function f(x) is horizontally stretched by factor $\dfrac{1}{k}$.

If $k>1$, the function f(x) is horizontally compressed by factor $\dfrac{1}{k}$.

We have,

$f(x)=x^2$

$g(x)=\left(\dfrac{1}{3}x\right)^2$

Using these functions, we get

$g(x)=f\left(\dfrac{1}{3}x\right)$         ...(ii)

On comparing (i) and (ii), we get

$k=\dfrac{1}{3}$

Since $0$, the function f(x) is horizontally stretched by factor $\dfrac{1}{\frac{1}{3}}=3$.

Hence, the correct option is D.