To determine the function that represents the cashier's earnings, we need to analyze the relationship between the number of hours worked and the earnings.
Given:
- The cashier earns \$7 per hour.
- [tex]\( x \)[/tex] is the number of hours worked.
To find the total earnings, [tex]\( y \)[/tex], we multiply the hourly wage by the number of hours worked.
This relationship can be mathematically described with the following function:
[tex]\[ y = 7 \times x \][/tex]
Let's evaluate the other options to ensure this is the correct one:
1. [tex]\( y = 7x \)[/tex]: This implies the total earnings [tex]\( y \)[/tex] are directly proportional to [tex]\( x \)[/tex] with a proportionality constant of 7, which matches our scenario.
2. [tex]\( y = x^7 \)[/tex]: This would imply an exponential increase in earnings with respect to hours worked, which doesn't fit our description since earnings increase linearly, not exponentially.
3. [tex]\( y = \frac{7}{x} \)[/tex]: This would imply that earnings decrease as the number of hours worked increases, which does not align with the straightforward linear relationship described.
4. [tex]\( y = 7 \)[/tex]: This would imply that the earnings are constant regardless of the number of hours worked, which also does not fit the hourly wage scenario.
Based on the analysis, the correct function representing the cashier's earnings is:
[tex]\[ y = 7x \][/tex]
So the choice that correctly represents this function is:
[tex]\[
y = 7x
\][/tex]
