Question

Maria earns an hourly wage of $10. She drew the following graph to show the relation of her income as a function of the hours she works. How did she modify the identity function to create her graph?

A) She multiplied the identity function by 10.
B) She added a constant of $10 to the identity function.
C) She divided the identity function by 10.
D) She subtracted a constant of $10 from the identity function.

Answer 1

Maria modified the identity function to show her income by multiplying the function by 10. This adjustment reflects her hourly wage, making her graph a straight line where each hour worked corresponds to a $10 increase in income.

Step-by-step explanation:

The student's question is about how Maria modified the identity function to create a graph that represents her income as a function of the hours she works. The identity function is a straight line that passes through the origin with a slope of 1, meaning that for every increase in x, there is an equal increase in y.

Maria earns $10 per hour, so for every hour she works, her income increases by $10. Therefore, to represent her income as a function of hours worked, she would need to modify the identity function so that for every unit (hour) increase on the x-axis, there is a $10 increase on the y-axis. This aligns with option A: She multiplied the identity function by 10. This means if Maria works for 2 hours, she earns $20 (2 hours * $10/hour), and the point (2, 20) would lie on the modified graph.