Which of the following is the independent variable in the equation below?
F(x)=5x+10
A.
10
B.
F
C.
5
D.
x
The Correct Answer and Explanation is:
The independent variable in the equation F(x)=5x+10F(x) = 5x + 10F(x)=5x+10 is xxx. Here’s an explanation of why:
In mathematics, an independent variable is a variable that represents the input of a function or the variable that is manipulated to observe changes in the dependent variable. In the context of the equation F(x)=5x+10F(x) = 5x + 10F(x)=5x+10, xxx is the independent variable.
Understanding the Equation:
- Function Definition: The equation F(x)=5x+10F(x) = 5x + 10F(x)=5x+10 defines a function FFF of xxx. The notation F(x)F(x)F(x) indicates that FFF is a function where xxx is the input variable.
- Role of xxx: In this function, xxx is the independent variable because you can choose different values for xxx and then calculate F(x)F(x)F(x). For each value of xxx, there is a corresponding value of F(x)F(x)F(x). Thus, xxx is the variable you change to see how it affects F(x)F(x)F(x).
The Dependent Variable:
- Function Output: The expression 5x+105x + 105x+10 represents how the dependent variable F(x)F(x)F(x) changes in response to changes in xxx. As xxx varies, the value of F(x)F(x)F(x) changes accordingly. Therefore, F(x)F(x)F(x) is dependent on xxx, making F(x)F(x)F(x) the dependent variable.
Why Not the Other Options:
- 10 (Option A): This is a constant term added to 5x5x5x but does not vary; hence, it is not a variable.
- F (Option B): In the function notation F(x)F(x)F(x), FFF represents the function itself, not a variable.
- 5 (Option C): This is a coefficient of xxx, not a variable. It scales the impact of xxx on F(x)F(x)F(x).
In summary, the independent variable in the function F(x)=5x+10F(x) = 5x + 10F(x)=5x+10 is xxx, as it is the variable that you can change and that determines the value of the dependent variable F(x)F(x)F(x).