1.7. An Introduction to Functions
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1.7. An Introductio n to Functions
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1.7. An Introduction to Functions. Goal 1: Input-Output Tables. A function is a rule that establishes a relationship between two quantities, called the input and the output . Input-Output Tables. For each input, there is exactly one output. - PowerPoint PPT Presentation
Transcript of 1.7. An Introduction to Functions
1.7. An Introduction
to Functions
Goal 1: Input-Output Tables
A function is a rule that establishes a relationship between two quantities, called the input and the output.
Input-Output Tables
1. For each input, there is exactly one output.
2. More than one input can have the same output.
0 31 134 2
Input-Output Table
One way to describe a function is to make an input-output table.
Input 0 1 3 4
Output 3 1 1 2
Input-Output Tables
Domain: The collection of all input values
Range: The collection of all output values
Making an Input-Output TableHere are 5 triangles:
1. Make an input-output table in which the input is the Figure Number and the output is the Triangle Number.
2. Does the table represent a function?
3. Describe Domain and Range.
1 2 3
4 5
Using a Table to Graph a Function
You are at an altitude of 250 feet in a hot-air balloon. You turn on the burner and rise at a rate of 20 feet per minute for 5 minutes. Your altitude h after you have risen for t minutes is
given by the function.
h = 250 + 20t
Step 1
For several inputs t, use the function to calculate an output h.
Example: t = 1h = 250 + 20(1)h = 250 + 20h = 270
Step 2
Organize the Data input an input-output table.
t minutes h altitude1 270234
Step 3
Graph the data in the table.
Altitude(h)
Time(t)
100
200
300
Step 4
What is the domain of the function?
What part of the domain is shown in the table?
Describing a Function
We have illustrated that functions can be described in these ways:
1. Input-Output Table2. Description in Words3. Equation4. Graph
Complete the Sentence
A function is a relationship between two quantities,
called the __________ and the _________.
Complete the Sentence
A function is a relationship between two quantities, called the Input and the
Output.
Complete the Sentence.
The collection of all input values is the ____________.
Complete the Sentence.
The collection of all input values is the domain.
Complete the Sentence.
The collection of all output values is the _________ of the function.
Complete the Sentence.
The collection of all output values is the range of the function.
Complete the Sentence
Four ways to represent a function are
(1) ____________________________(2) ____________________________(3) ____________________________(4) ____________________________
Complete the Sentence
Four ways to represent a function are
(1) Input-Output Table(2) Words(3) Equation (4) Graph
Does the Table Represent a function?
Input Output1 32 43 54 6
Does the Table Represent a function?
Input Output1 32 43 54 6
Yes; for each input, there is exactly one output.
Does the Table Represent a function?
Input Output1 32 33 44 4
Does the Table Represent a function?
Input Output1 32 33 44 4
Yes; for each input, there is exactly 1 output.
Does the Table Represent a function?
Input Output1 31 43 54 6
Does the Table Represent a function?
Input Output1 31 43 54 6
No; there are 2 output values that correspond to the input value 1.
Make an input-output table for the function. Use 0, 1, 2, and 3 as the domain.
y = 3x + 2
Make an input-output table for the function. Use 0, 1, 2, and 3 as the domain.
y = 3x + 2Output: 2, 5, 8, 11
