Let's solve the problem step by step.
1. Identify the Input and Output Values:
The function provided is [tex]\( y = 40m + 60 \)[/tex].
- The input value [tex]\( m \)[/tex] represents the number of months.
- The output value [tex]\( y \)[/tex] represents the total cost.
Therefore:
- The input values for this function are months.
- The output values for this function are total cost.
2. Calculate the Total Cost for 9 Months:
According to the given function [tex]\( y = 40m + 60 \)[/tex], let's substitute [tex]\( m = 9 \)[/tex]:
- Total cost [tex]\( y = 40 \times 9 + 60 \)[/tex]
- Total cost [tex]\( y = 360 + 60 \)[/tex]
- Total cost [tex]\( y = 420 \)[/tex]
After 9 months, the total cost will be \[tex]$ 420.
3. Determine the Appropriate Scales for the Axes:
- Since we're considering a number of months (ranging from 0 up to at least 9), a reasonable scale for the \( x \)-axis (months) would be from 0 to 12 months to cover enough range.
- Given that each month costs \$[/tex] 40 and the initial cost of the cell phone is \$ 60, we need a scale that accommodates the total cost. For up to 12 months, the formula [tex]\( y = 40m + 60 \)[/tex] gives a maximum value of [tex]\( y = 40 \times 12 + 60 = 480 \)[/tex]. Therefore, an appropriate scale for the [tex]\( y \)[/tex]-axis (total cost) would be from 0 to 500 dollars.
4. Summary of Answer:
- The input values for this function are months.
- The output values for this function are total cost.
- An appropriate scale for the [tex]\( x \)[/tex]-axis would be: 0 to 12 months.
- An appropriate scale for the [tex]\( y \)[/tex]-axis would be: 0 to 500 dollars.
