Question

Suppose f(x)= x^2 and g(x)= (1/5x)^2. Which statement best compares the graph of g(x) with the graph of f(x)?

Answer 1

Answer:

A is correct

The graph g(x) is the graph of f(x) horizontally stretched by factor of 5.

Step-by-step explanation:

We are given two function f(x) and g(x). We need to compare both functions using graph.

$f(x)=x^2$

$g(x)=\left(\frac{1}{5}x\right)^2$

If we compare f(x) and g(x)

$f(\frac{1}{5}x)=\left(\frac{1}{5}x\right)^2=g(x)$

So, here change in coefficient of x

If y=f(x) then y=f(ax)

Horizontal stretch/compress by factor of a

If a>1 then stretch

If 0<a<1 then compress

Here a is 0.2<1

Therefore, g(x) is stretch horizontally by factor of 5

Thus, The graph g(x) is the graph of f(x) horizontally stretched by factor of 5.

Answer 2

The graph is horizontally stretched by a factor of 1/5 because you are literally multiplying x by 1/5. So, your answer is A. Hope it makes sense.