A.4.2.2 A Handy Notation

Author:Katie Akesson

One way to talk about functions precisely and without wordy descriptions is by naming the functions and using 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 output value 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.

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.

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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"

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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"

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A.4.2.2 A Handy Notation

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