Write y = 2x + 3 using function notation. A) x = 2y + 3 B) f(y) = 2x + 3 C) f(x) = 2x + 3 D) f(y) = 2y + 3
The Correct Answer and Explanation is:
The correct answer is C) f(x) = 2x + 3.
Explanation:
In mathematics, function notation is used to represent functions in a more compact and organized form. A function describes a relationship where each input (typically denoted as x) is associated with exactly one output (denoted as f(x), which is the value of the function at x).
Let’s break down the options:
- Option A: x = 2y + 3
- This option is incorrect because it doesn’t use proper function notation. It represents a linear equation, but it’s solving for x in terms of y, which doesn’t follow the structure of a function where the output is written as a function of the input.
- Option B: f(y) = 2x + 3
- This is also incorrect. The variable inside the function notation should match the variable used in the equation. In the original equation y = 2x + 3, y is the dependent variable, and x is the independent variable. The function should express y in terms of x (not y in terms of x). This would be valid if the equation were reversed (for example, x = 2y + 3).
- Option C: f(x) = 2x + 3
- This is the correct answer. Here, f(x) represents the function where x is the input, and the output is given by 2x + 3. This is simply the equation y = 2x + 3 rewritten in function notation, where y is replaced by f(x). The variable f(x) indicates that the value of y is determined by the function of x.
- Option D: f(y) = 2y + 3
- This option is incorrect because it reverses the roles of the variables. It implies that y is the independent variable, but in the given equation, x is the independent variable, and y depends on x.
In summary, f(x) = 2x + 3 is the correct function notation that represents the equation y = 2x + 3, where f(x) is the function output corresponding to the input x.
