Concept: Introduction to Functions EQ: How do we interpret and represent functions using function notation? (F.IF.2) Vocabulary: Function notation, f(x), Domain, Range Lesson 3.2 – Function Notation

Activating Strategy  Do you have a nickname? If so, raise your hand to share it with us.  How do you think a nickname and function notation are related?

Introduction  Recall that in a function, every element of the domain is paired with exactly one element of the range. That is, for every value of x, there is exactly one value of y.  Today, we will learn about Function notation.

Introduction, continued  Function notation is a way to name a function using f(x) instead of y. To make a general statement, we call the process by a letter, such as f, and we can call the results of that process “f of x.” We write “f of x” as f(x).  Functions can be named using any letter, though f and g are used often. Using function notation, we can graph more than one function at a time. If we call one function f and another g, then we can graph y = f(x) and y = g(x) on the same coordinate plane.

Key Concepts

Key Concepts, continued  For example, let f be a function with the domain {1, 2, 3} and let f(x) = 2x. To evaluate f over the domain {1, 2, 3}, we would write the following equations by substituting each value in the domain for x:  f(1) = 2(1) = 2  f(2) = 2(2) = 4  f(3) = 2(3) = 6 {2, 4, 6} is the range of f(x).

Steps for Evaluating Functions Step 1: Evaluate the function over the domain by substituting the values from the domain into the function. Step 2: Collect the set of outputs from the inputs. (Your answers from step 1 will become your outputs, or range).

Example 1:

Example 1, continued

You Try!

Example 2

Example 2, continued

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Example 3

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Example 4

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Summary:  List 3 main things you know about function notation, give 2 examples of function notation, and 1 question you have about function notation.