Activity
Let’s name the functions that relate the dog’s distance from the post and the time since its owner left: function for Day 1, function for Day 2, function for Day 3. The input of each function is time in seconds, .
Day 1
Day 2
Day 3
Use function notation to complete the table.
Day 1 | Day 2 | Day 3 | |
a. distance from post 60 seconds after the owner left | |||
b. distance from post when the owner left | |||
c. distance from post 150 seconds after the owner left |
1. Use function notation to represent the dog's distance from the post 60 seconds after the owner left.
a. Enter your answer for Day 1:
Compare your answer:
b. Enter your answer for Day 2:
Compare your answer:
c. Enter your answer for Day 3:
Compare your answer:
2. Use function notation to represent the dog’s distance from the post when the owner left.
a. Enter your answer for Day 1:
Compare your answer:
b. Enter your answer for Day 2:
Compare your answer:
c. Enter your answer for Day 3:
Compare your answer:
3. Use function notation to represent the dog’s distance from the post 150 seconds after the owner left.
a. Enter your answer for Day 1:
Compare your answer:
b. Enter your answer for Day 2:
Compare your answer:
c. Enter your answer for Day 3:
Compare your answer:
4. Describe what each expression represents in this context:
a.
Compare your answer:
is the distance from the post 15 seconds after the owner left on Day 1.
b.
Compare your answer:
is the distance from the post 48 seconds after the owner left on Day 2.
c.
Compare your answer:
is the distance from the post seconds after the owner left on Day 3.
5. The equation can be interpreted to mean: “On Day 2, 120 seconds after the dog owner left, the dog was 4 feet from the post.” Describe what each equation represents in this context.
a.
Compare your answer:
On the third day, 40 seconds after the owner left, the dog was 4.6 feet away from the post.
b.
Compare your answer:
On the first day, seconds after the owner left, the dog was 5 feet away from the post.
c.
Compare your answer:
On the second day, seconds after the owner left, the dog was feet away from the post.
Video: Interpreting Function Notation
Watch the following video to learn more about function notation.
Self Check
Additional Resources
Understanding Function Notation
Using Function Notation
Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.
To represent “height is a function of age,” we start by identifying the descriptive variables for height and for age. The letters , , and are often used to represent functions, just as we use , , and to represent numbers and , , and to represent sets.
- is of : We name the function ; height is a function of age.
- : We use parentheses to indicate the function input.
- : We name the function ; the expression is read as “ of .”
Remember, we can use any letter to name the function; the notation shows us that depends on . The value must be put into the function to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.
We can also give an algebraic expression as the input to a function. For example, means “first add and , and the result is the input for the function .” The operations must be performed in this order to obtain the correct result.
Function Notation
The notation defines a function named . This is read as “ is a function of .” The letter represents the input value, or independent variable. The letter , or , represents the output value, or dependent variable.
Example: Using Function Notation for Days in a Month
Use function notation to represent a function whose input is the name of a month and output is the number of days in that month (don’t include leap years).
For example, (March), because March has 31 days. The notation reminds us that the number of days, (the output), is dependent on the name of the month, (the input).
Analysis
Note that the inputs to a function do not have to be numbers; function inputs can be names of people, labels of geometric objects, or any other element that determines some kind of output. However, most of the functions we will work with in this course will have numbers as inputs and outputs.
Try it
Try It: Understanding Function Notation
Use function notation to express the weight of a pig, , in pounds as a function of its age in days, .
Compare your answer. Here is how to express this situation in function notation:
. The pig’s weight is a function of the age of the pig in days.