Answer:
The equation of the graph g(x) is g(x) = [tex]\frac{1}{3}[/tex] 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) = [tex]\frac{1}{3}[/tex] x²
∵ x = 3
∴ g(3) = [tex]\frac{1}{3}[/tex] (3)²
∴ g(3) = [tex]\frac{1}{3}[/tex] (9)
∴ g(3) = 3
∴ g(x) = [tex]\frac{1}{3}[/tex] x²
Lets check the other answers
If g(x) = [tex]\frac{1}{9}[/tex] x²
∵ x = 3
∴ g(3) = [tex]\frac{1}{9}[/tex] (3)²
∴ g(3) = [tex]\frac{1}{9}[/tex] (9)
∴ g(3) = 1
∴ g(x) ≠ [tex]\frac{1}{9}[/tex] x²
If g(x) = [[tex]\frac{1}{3}[/tex] x]²
∵ x = 3
∴ g(3) = [ [tex]\frac{1}{3}[/tex] (3)]²
∴ g(3) = [ [tex]\frac{1}{9}[/tex] (9)]
∴ g(3) = 1
∴ g(x) ≠ [[tex]\frac{1}{3}[/tex] 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) = [tex]\frac{1}{3}[/tex] x²
