Graphs of Quadratic Relationships:
If [tex]f(x)=x^2[/tex], which equation represents function [tex]g[/tex]?
A. [tex]g(x)=\frac{1}{3} f(x)[/tex]
B. [tex]g(x)=3 f(x)[/tex]
Answer (1)
Substitute f ( x ) = x 2 into the given options for g ( x ) .
Option A: g ( x ) = 3 1 f ( x ) = 3 1 x 2 .
Option B: g ( x ) = 3 f ( x ) = 3 x 2 .
Without a graph or further information about g ( x ) , we cannot definitively choose between options A and B. The question is incomplete.
Explanation
Understanding the Problem We are given the function f ( x ) = x 2 and two possible equations for a function g ( x ) : A. g ( x ) = 3 1 f ( x ) and B. g ( x ) = 3 f ( x ) . We need to determine which equation represents the function g ( x ) . Unfortunately, we do not have enough information to determine the correct answer. Without a graph or some other property of g ( x ) , we cannot definitively choose between options A and B.
Substituting f(x) Let's substitute f ( x ) = x 2 into the given options for g ( x ) .
Option A: g ( x ) = 3 1 f ( x ) = 3 1 x 2 .
Option B: g ( x ) = 3 f ( x ) = 3 x 2 .
Conclusion Since we don't have a graph or any other information about g ( x ) , we cannot definitively choose between options A and B. The question is incomplete.
Examples
Consider the function f ( x ) = x 2 , which represents the area of a square with side length x . If we want to create a new function g ( x ) that represents the area of a square with sides three times as long, we would use g ( x ) = 3 f ( x ) = 3 x 2 . This shows how scaling a function can relate to real-world geometric transformations.
