Question

Suppose f(x)=x^2. What is the graph of g(x)=f(5x)?
Can some please help me

Answer 1

The answer is D

Explanation:

* Lets revise some transformations

- A horizontal compression is the squeezing of the graph toward

the y-axis.

- If the graph is y = f(x) and its image is y = f(k•x)

∴ The graph is horizontally compressed if k > 1 that means divide

each of its x-coordinates by k.

∴ The graph is horizontally stretched if 0 < k < 1, that means divide

each of its x-coordinates by k.

* Now lets solve the problem

∵ f(x) = x²

∵ g(x) = f(5x)

- Substitute the value of x in f(x) by 5x

∴ f(5x) = (5x)²

∴ g(x) = (5x)²

∵ The image of f(x) = x² is g(x) = (5x)²

∴ k = 5

∵ 5 > 1

∴ The graph of f(x) is compressed horizontally

- divide each x-coordinates of the points on the graph by 5

∴ The graph becomes narrow to the y-axis

- Look to the attached graph for more understanding

# The red graph is f(x) = x²

# The blue graph is g(x) = (5x)²

* The answer is the last graph D

Answer 2

Option D.

EXPLANATION

The given function is

`f(x) = {x}^(2)`

The new function is

`g(x) = f(5x)`

This implies that,

`g(x) = {(5x)}^(2)`

This gives us:

`g(x) = {25x}^(2)`

We can that the graph of g(x) will shrink by a factor of 25 compared to f(x).

The graph will open upwards and shrink towards the y-axis.