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 mathematical notation, when we write an equation like y=2x+3y = 2x + 3y=2x+3, we are expressing yyy as a function of xxx. To rewrite this in function notation, we replace yyy with f(x)f(x)f(x), where fff represents the function and xxx is the input variable.
Function notation is used to show that the value of yyy depends on xxx. In this case, the function can be written as:f(x)=2x+3f(x) = 2x + 3f(x)=2x+3
This means that for any value of xxx, you can find f(x)f(x)f(x) (or yyy) by substituting xxx into the equation.
Why the other options are incorrect:
- A) x = 2y + 3: This reverses the relationship and incorrectly expresses xxx as a function of yyy. It also doesn’t follow the given equation.
- B) f(y) = 2x + 3: This notation suggests that yyy is the independent variable (input) and xxx is the dependent variable (output), which does not reflect the original equation y=2x+3y = 2x + 3y=2x+3.
- D) f(y) = 2y + 3: Again, this incorrectly uses yyy as the input to the function. It changes the relationship between xxx and yyy that was defined in the original equation.
Thus, C) f(x) = 2x + 3 is the correct form of the given equation in function notation.
