# A.4.2.2 A Handy Notation

- Author:
- Katie Akesson

**function notation**. • Suppose we give a name to each function that relates the dog’s distance from the post and the time since the dog owner left: function f for Day 1, function g for Day 2, function h for Day 3. The input of each function is time in seconds, t. • To represent “the distance of the dog from the post 60 seconds after the owner left,” we can simply write: f(60) - read "f of 60". To express the same quantity for the second and third day, we can write g(60) - read "g of 60" and h(60) - read "h of 60". • f(60) does not simply that 60 seconds have passed, but instead the expression

**f(60) represents the**of the function when 60 seconds have passed. In this case, it means the dog’s distance from the post, on Day 1, 60 seconds after its owner left.

*output**value*Let’s name the functions that relate the dog’s distance from the post and the time since its owner left: function f for Day 1, function g for Day 2, function h for Day 3. The input of each function is time in seconds, t. Use function notation to complete the table below.

Describe what each expression represents in this context: a. f(15) - read as "f of 15" b. g(48) - read as "g of 48" c. h(t) - read as "h of t"

The equation g(120) = 4 can be interpreted to mean: “On Day 2, 120 seconds after the dog owner left, the dog was 4 feet from the post.” What does each equation mean in this situation? a. h(40) = 4.6 - read as "h of 40 equals 4.6" b. f(t) = 5 - read as "f of t equals 5" c. g(t) = d - read as "g of t equals d"