Question

Please help :( I would appreciate it so much ​

Answer 1

Answer:

The equation of the graph g(x) is g(x) =  $\frac{1}{3}$ x² ⇒ A

Step-by-step explanation:

∵ f(x) = x²

∵ Point (3 , 3) lies on g(x)

- To find the equation of g(x) substitute x by 3 in each equation

    and find which one will give y = 3

If g(x) = $\frac{1}{3}$ x²

∵ x = 3

∴ g(3) = $\frac{1}{3}$ (3)²

∴ g(3) = $\frac{1}{3}$ (9)

∴ g(3) = 3

∴ g(x) = $\frac{1}{3}$ x²

Lets check the other answers

If g(x) = $\frac{1}{9}$ x²

∵ x = 3

∴ g(3) = $\frac{1}{9}$ (3)²

∴ g(3) = $\frac{1}{9}$ (9)

∴ g(3) = 1

∴ g(x) ≠ $\frac{1}{9}$ x²

If g(x) = [$\frac{1}{3}$ x]²

∵ x = 3

∴ g(3) = [ $\frac{1}{3}$ (3)]²

∴ g(3) = [ $\frac{1}{9}$ (9)]

∴ g(3) = 1

∴ g(x) ≠  [$\frac{1}{3}$ x]²

If g(x) = 3x²

∵ x = 3

∴ g(3) = 3(3)²

∴ g(3) = 3(9)

∴ g(3) = 27

∴ g(x) ≠ 3x²

The equation of the graph g(x) is g(x) =  $\frac{1}{3}$ x²