Answer:
The answer is D
Step-by-step 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
