Question

What is another way to write the function rule f(x) = x^2 - 3?

Option 1: 2 = y^2 - 3
Option 2: y = z? - 3
Option 3: f(3) = y^2 - 3
Option 4: f(y) = x² - 3

Answer 1

The correct answer is Option 4: f(y) = y^2 - 3, which properly rewrites the original function f(x) = x^2 - 3 by changing the variable from x to y while maintaining the function's structure.

Step-by-step explanation:

The student is asking to find another way to write the function rule f(x) = x^2 - 3. In mathematics, especially when dealing with functions, it is important to maintain the structure of the function while ensuring that the variables and function notation properly convey the same relationship. Looking at the options provided:

• Option 1: is incorrect because it replaces f(x) with 2, which changes the meaning.
• Option 2: introduces a new variable z without explaining the relationship to x or y.
• Option 3: is incorrect because it presents f(3) as a function of y, which confuses the function evaluation with the function definition.
• Option 4: is correct as it maintains the function structure while changing the variable from x to y. This implies f(y) = y^2 - 3, which is a valid transformation of the original function rule.

Therefore, the correct answer is Option 4: f(y) = y^2 - 3.