Question

Select the correct answer from each drop down menu

Function g is a
1.horizontal translation
2.vertical translation
3.reflection
4.dialation

G(x)=
1.4
2. 2
3. -1/4
4. 1/4

Answer 1

g(x) is a dilation of function f(x), and
`g(x) = (1)/(4)x^2`

Explanation:

Function f is
`f(x) = x^2`

So:

When
`x = 0, f(x) = 0`

When
`x = 1, f(x) = 1`

When
`x = 2, f(x) = 4`

When
`x = 3, f(x) = 9`

Now

For function g, looking at the graphic, we have that:

When
`x = 0, g(x) = 0`

When
`x = 2, g(x) = 1`

When
`x = 3, g(x) = 2.5`

That is, g(x) is a fourth of f(x).

This means that we have a dilation by a factor of 1/4, so
`g(x) = (1)/(4)x^2`