Question

F(x) = x^2. What is g(x)?

Answer 1

The correct answer is C. g(x) = 1/4x^2

Explanation:

In order to determine if the graph fits, take the point that is given on the parabola and see if it fits the equation. To do that we plug it in and see if it gives a true statement.

(2, 1)

g(x) = 1/4x^2

1 = 1/4(2)^2

1 = 1/4(4)

1 = 1 (TRUE)

Answer 2

C, g(x) = 1/4x²

Explanation:

the parent function of g(x) is the function f(x) = x² as shown on the graph

with the coefficient 1/4 in front of the parent function, we can determine its transformation.

it is a vertical shrink by 1/4 of the original graph. the reason why we know this is because a vertical shrink/stretch has a coefficient on the outside of the parent function (as shown in g(x)) and if we follow the rule:

b > 0 < this is a vertical stretch

b < 0 < this is a vertical shrink

b in this function is 1/4, which is less than 0