Unit 2 Lesson 1 Function Definitions

Function vs. Relation Function: Is a special relation in which each input gives only one output. Relation: Is a comparison of two numbers. Examples: {(1, 2), (2, 3), (3, 4)} notice each input has only one output! {(1, 2), (2, 2), (3, 2)} again notice how each input has only one output. Examples: {(1, 3), (1, 4), (2, 5)} notice how the input 1 has two different outputs, this is not a function, but it is a relation. {(1, 2), (1, 3), (1, 4)} again notice how the same input has different outputs.

Parts of a function Domain: The domain of a function is the list of all possible input values. Range: The range of a function is the list of all possible output values. Example: {(1,2), (2, 3), (3, 4)} is a function. The domain of the function is the list of the inputs : {1, 2, 3} The range of the function is the list of the outputs: {2, 3, 4}

Function notation We often use f(x) (say “f of x”) to represent functions. For example: f(x) = 2x is a definition of a function. In this definition, each input is multiplied by 2 in order to arrive at an output. Using function notation allows us to use function rules to find input and output values.

Function notation continued… Example: Let f(x) = 3x + 1. Find f(4). *f(4) means to evaluate the function for the input value of 4* Substituting 4 for x we now have: f(4) = 3(4) + 1 f(4) = 12 + 1 = 13 f(4) = 13 We can also write the solution as the ordered pair (4, 13).

Your turn Evaluate the following function rules for the given input values 1. f(x) = 3x – 4, find f(2). 2. g(x) = -2x + 7, find g(7).

Solutions 1. f(2) = 2 2. g(7) = -7

Next steps…. Be sure to watch the videos for this lesson! Also, take the quiz with this lesson.