Unit 5, Lesson 4
Using Function Notation to Describe Rules (Part 1)
Algebra 1
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A square that has a side length of 9 cm has an area of 81 cm2. The relationship between the side length and the area of the square is a function.
Complete the table with the area for each given side length.
Then, write a rule for a function, , that gives the area of the square in cm2 when the side length is cm. Use function notation.
| side length (cm) | area (cm2) |
|---|---|
| 1 | |
| 2 | |
| 4 | |
| 6 | |
On the coordinate plane, sketch a graph of this function.
A roll of paper that is 3 feet wide can be cut to any length.
If we cut a length of 2.5 feet, what is the perimeter of the paper?
Complete the table with the perimeter for each given side length.
Then, write a rule for a function, , that gives the perimeter of the paper in feet when the side length in feet is . Use function notation.
| side length (feet) | perimeter (feet) |
|---|---|
| 1 | |
| 2 | |
| 6.3 | |
| 11 | |
On the coordinate plane, sketch a graph of this function.
Some functions are defined by rules that specify how to compute the output from the input. These rules can be verbal descriptions or expressions and equations. For example:
Rules in words:
Rules in function notation:
Some functions are defined by rules that relate two quantities in a situation. These functions can also be expressed algebraically with function notation.
Suppose function gives the cost of buying pounds of apples at \$1.49 per pound. We can write the rule to define function .
To see how the cost changes when changes, we can create a table of values.
| pounds of apples, | cost in dollars, |
|---|---|
| 0 | 0 |
| 1 | 1.49 |
| 2 | 2.98 |
| 3 | 4.47 |
Plotting the pairs of values in the table gives us a graphical representation of .