Example Question #1 : Interpret Statements That Use Function Notation In Terms Of A Context
Consider the scenario below:
Helen is a painter. It takes her 3 days to make each painting. She has already made 6 paintings. Which of the following functions best models the number of paintings she will have after days?
The question asks, "Which of the following functions best models the number of paintings she will have after days?"
From this, you know that the variable represents the number of days, and that represents the number of paintings she makes as a function of days spent working.
If it takes 3 days to make a painting, each day results in paintings. Therefore, we have a linear relationship with slope .
Additionally, she begins with 6 paintings. Therefore, even when zero days are spent working on paintings, she will have 6 paintings. In other words, . This means the y-intercept is 6.
As a result, the function will be
which can be rewritten as
Example Question #2 : Interpret Statements That Use Function Notation In Terms Of A Context
The daily pay in U.S. Dollars for a certain job is defined as the following function , where equals time in hours:
If an employee works for 7 hours in a day, how much is he or she paid?
The above function can be understood as, "An employee is paid $15 for each hour he or she works, plus a flat amount of $10."
If an employee works 7 hours, we can find the amount that he or she is paid by plugging in 7 for "Hours" in the equation:
Adhering to order of operations, we next find the product of 15 and 7:
Finally, we find the sum of 105 and 10:
The employee is paid $115.00 for seven hours' work.