Question

Question Stem
1) You have just been offered a job at the
Carmax Dealership! The manager tells you that
you will be getting paid \$13.50 an hour. She
also tells you that you will be working anywhere
from 40-45 hours weekly. Your weekly pay
can be determined by the function
P(t)
13,50t, where t is the time in hours.
Find a reasonable range for this scenario.
A. {540, 553.5, 567, 580.5, 594, 607.5}
B. 0≤ y ≤45
C. 40 ≤ x ≤ 45
D. 540 ≤ y ≤ 607.5
Student Work
Is this scenario continuous or discrete?
How do you know?
Create a table of the data points we know

1. hongcuc2
The range for the given scenario is  {540, 553.5, 567, 580.5, 594, 607.5} and this is continuous.

### What is the range of a function?

A function is defined as follows:
f(x) = y
Where x is the input variable and y is the output variable
Then the set of output values for the set of input values is said to be the range of the function.

### Calculation:

The given function is P(t) = 13.50t
Where t is the input variable. The variable ‘t’ represents the working hours.
The given interval for t is 40 – 45 hours weekly.
Then the output values for the given interval of input values are:
for t = {40, 41, 42, 43, 44, 45};
P(40) = 13.50(40) = 540
P(41) = 13.50(41) = 553.5
P(42) = 13.50(42) = 567
P(43) = 13.50(43) = 580.5
P(44) = 13.50(44) = 594
P(45) = 13.50(45) = 607.5
Then the range for the given scenario is {540, 553.5, 567, 580.5, 594, 607.5}.
Since the difference between each value is the same i.e.,
553.5 – 540 = 13.5 or 567 – 553.5 = 13.5 and so on.
So, this scenario is continuous.