Certainly! Let's identify the independent variable in the given function.
The function provided is [tex]\( P(x) = 1250 + 0.08x \)[/tex], which describes Robert's monthly pay based on his total sales.
1. Understand the Function:
- In this function, [tex]\( P(x) \)[/tex] represents Robert's monthly pay.
- The value [tex]\( 1250 \)[/tex] is a fixed component of his salary.
- The term [tex]\( 0.08x \)[/tex] represents the [tex]$8\%$[/tex] commission on his total sales, [tex]\( x \)[/tex].
2. Determine the Variables:
- [tex]\( P(x) \)[/tex] is the dependent variable since it depends on the value of [tex]\( x \)[/tex] (total sales).
- The [tex]\( 0.08 \)[/tex] representing the commission rate is a constant multiplier.
- The [tex]\( x \)[/tex] in the term [tex]\( 0.08x \)[/tex] represents his total sales.
3. Identify the Independent Variable:
- The independent variable is the one that we can change or control directly to see its effect on the dependent variable.
- In this function, [tex]\( x \)[/tex] is the independent variable because it represents the total sales, which directly affects the monthly pay [tex]\( P(x) \)[/tex].
Thus, the independent variable of the function [tex]\( P(x) = 1250 + 0.08x \)[/tex] is the total sales [tex]\( x \)[/tex].
Therefore, the independent variable is sales.
