Question

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

A. the graph of g(x) is shifted 2 units to the right.
B. the graph of g(x) is horizontally stretched by a factor of 2
C. the graph of g(x) is vertically compressed by a factor of 2
D. the graph of g(x) is horizontally compressed by factor of 2

Answer 1

Option B

Explanation:

If we have a function f(x) and perform the following operation on the function:

`y = f(bx)`

Where b is a positive real number that complies with
`0 <b <1`

Then the function f (x) is stretched horizontally by a factor of
`(1)/(b)`.

In this problem we perform the function:

`f(x) = x ^ 2\\\\g(x) = ((1)/(2)x) ^ 2`

So, in this case
`b = (1)/(2)`.. This means that g(x) is the function f(x) stretched on the x axis by a factor of 2 units.

Therefore the correct option is:

B. the graph of g(x) is horizontally stretched by a factor of 2