Lesson 5: 1-7 Functions

What is the definition of a function?
When you are looking at a graph, how do you know if it is a function?

Function
Discrete Function
Continuous Function
Vertical line test
Function Notation
Nonlinear Function

F.IF.1
A. Understand the concept of a function and use function notation
1. HSF-IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of
the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the
equation y = f(x).

2. HSF-IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

B. Interpret functions that arise in applications in terms of the context
5. HSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.?

Chapter 1A (1-1 - 1-4) (Skip 1-3) 1B (1-6-1-8 skip end behavior) (Skip 1-5)

A function is a relationship between input and output in which each input value has exactly one output. The set of input values is the domain of the function and the set of output values is the range of the function. A vertical line test can be used to check if a graph is a function. The graph of a discrete function consists of points that are not connected, but the graph of a continuous function forms a line or smooth curve.

The distance a car travels from when the brakes are applied to the car's complete stop is the stopping distance. This includes time for the driver to react. The faster a car is traveling the longer the stopping distance. The stopping distance is a function of the speeed of the car.

Function notation is sometimes difficult for student to comprehend. Stress that f(x) does not mean "f times x."

Error Analysis For Exercise 54, Corazon forgot that each point in the table would have to correspond to a point on the graph for them to be the same.

If students are visual learners, have students represent several nonlinear functions graphically to share with the class.

Formative assessment: Exercises 1-19

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