Activity
1. A square that has a side length of 9 cm has an area of 81 . The relationship between the side length and the area of the square is a function.
For questions a-e use the table by answering each question.
Side Length |
Area |
1 |
a. _______ |
2 |
b. _______ |
4 |
c. _______ |
6 |
d. _______ |
|
e. _______ |
a. What is the area in when the side length is ?
The area is 1 when the side length is .
b. What is the area in when the side length is ?
The area is 4 when the side length is .
c. What is the area in when the side length is ?
The area is when the side length is .
d. What is the area in when the side length is ?
The area is when the side length is .
e. Write a rule for a function, , that gives the area of the square in when the side length is .
Compare your answer:
f. What does represent in this situation? What is its value? Write your answers, then click solution to compare your answer.
Compare your answer:
is the area of the square in cm2 when the side length is 2 cm. Its value is 4.
g. Sketch a graph of this function. Use the desmos graphing tool or technology outside the course.
Compare your answer:
2. A roll of paper that is 3 feet wide can be cut to any length.
a. If we cut a length of 2.5 feet, what is the perimeter of the paper? Enter your answer in feet.Use integers only.
The perimeter of the paper is 11 feet.
For questions b-f, keep in mind that the roll of paper is 3 feet wide. Complete the table by answering each question.
side length (feet) | perimeter (feet) |
1 |
b. _______ |
2 |
c. _______ |
6.3 |
d. _______ |
11 |
f. _______ |
b. If we cut a length of 1 foot, what is the perimeter of the paper to the nearest whole foot?
The perimeter is 8 feet when the side length is .
c. To the nearest whole foot, what is the perimeter when the side length is 2 feet?
The perimeter is 10 feet when the side length is .
d. What is the exact perimeter, in feet, when the side length is 6.3 feet?
The perimeter is 18.6 feet when the side length is .
e. What is the perimeter, to the nearest whole foot,when the side length is 11 feet?
The perimeter is 28 feet when the side length is .
f. Write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is l.
Compare your answer:
g. What does P(11) represent in this situation? What is its value?
Compare your answer:
is the perimeter of the paper in feet when the paper is cut at a length of 11 feet. Its value is 28.
h. Sketch a graph of this function. Use the desmos graphing tool or technology outside the course.
Compare your answer:
Video: Writing Function Rules
Watch the following video to learn more about writing rules with function notation.
Self Check
Additional Resources
Write the Function Rule from a Table
Kelly can tune 6 cars in 3 hours. The table below is completed to show this relationship. The last column has the output for any . This is the rule of the function.
Time spent tuning cars () | 2 | 3 | 6 | 7 | |
Number of cars tuned up () | 4 | 6 | 12 | 14 |
Kelly can tune 6 cars in 3 hours or 2 cars in 1 hour, so the function rule is .
Try it
Try It: Write the Function Rule from a Table
Determine the rule in function notation for the table below:
(input) | 1 | 2 | 3 | 4 | |
(output) | 5 | 8 | 11 | 14 | ? |
Compare your answers:
Here is how to find the rule in function notation:
In the table, every is multiplied by 3, and then 2 is added. The rule is: