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Functions and Graphs
 A function is a rule in which each value assigned to the function (each input) produces exactly one output.
 Functions are graphed on the coordinate plane.
 The input value is called the independent variable and the output is called the dependent variable.
 A relation is a set of ordered pairs. The set of all first terms is called the domain of the relation. The set of second terms is called the range of the relation.
 A discrete function has a graph consisting of isolated points that are not connected.
 A continuous function has a graph that is a smooth curve or line.
Functions and Graphs
The function f is given by the table
Plot its graph






 







Plot its graph
 Find coordinate points
(1,5),(2,6),(3,7),(4,2),(5,0)
Chart the points
The function f is given by the table
Plot its graph






 







Plot its graph
 Find coordinate points
(1,1),(2,3),(3,5),(4,7),(5,9)
Chart the points
The function f is given by the table
Plot its graph






 







Plot its graph
 Find coordinate points
(  2,2),(  1,6),(0,  5),(1,  9),(2,8)
Chart the points
The function f is given by the table
Plot its graph






 







Plot its graph
 Find coordinate points
(0,  2),(3,  3),(  9,1),(  4,6),(7,5)
Chart the points
Suppose gas costs $4.00 per gallon. Make a table that shows the costs of buying gas from 1 to 5 gallons.
Create a table with gallons as independent and cost as dependent
Create a table with gallons as independent and cost as dependent
gallons line 1 2 3 4 5 cost line  Calculate the costs from the independent values






 







Consider the data found in the previous problem, and make a graph from the table
 Find the coordinate pairs from the table
(1,4),(2,8),(3,12),(4,16),(5,20)  Chart the graph with the appropriate dependent and independent axises
 Chart the graph with the coordinate points
A shipping company charges $3.50 per pound to send a package. The company rounds up to the next pound to calculate the cost, and maximum allowed weight is 9 pounds. What is the domain and range of of the function which represents the company's costs?
 Consider what values are dependent and independent
Domain (weight in pounds) = 0 < x ≤ 9
Range (cost in $ ) = { 3.5, 7, 10.5, ..., 31.5}
Range (cost in $ ) = { 3.5, 7, 10.5, ..., 31.5}
Consider the same shipping company from the previous question with the same costs. What are the first 5 ordered pairs from its data?
 Remember what's the domain and range of the function






 







Graph the company's shipping rates
 Utilize and expand the data from the previous problem
Another shipping company has a flat rate of $20.50 for shipping. If you were shipping a batch of cookies which weighed 5.5 pounds, should you use the original shipping company as described in the previous three questions?
 Remember the weight properties of the original the shipping company
No, because at 5.5 pounds the costs would be $21 which is more expensive.
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Answer
Functions and Graphs
Lecture Slides are screencaptured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
 Intro 0:00
 Functions 0:15
 Example: Function
 Example: Not Functions (Relations)
 Graphs 4:44
 Visual Display
 Example: X and Y
 Coordinate Pairs
 Discrete Function
 Continuous Function
 Vertical Line Test 10:55
 Test if Function
 Example: Pass Through Points
 Domain and Range 14:13
 Example
 Example 1: Function Given by Table 16:24
 Example 2: Cost of Gas 18:46
 Example 3: Cost of Gas 23:15
 Example 4: Cost of Mail 29:07
1 answer
Last reply by: Dr Carleen Eaton
Sun Feb 11, 2018 9:46 PM
Post by John Stedge on January 18 at 04:33:04 PM
The range would be {4,3,2,1} at 15:35 because you always write domain and range from least to greatest.
0 answers
Post by musse Wacays on July 26, 2015
okay
1 answer
Last reply by: Dr Carleen Eaton
Wed Jun 26, 2013 11:33 PM
Post by Taylor Wright on June 17, 2013
In example 3:
Couldn't X and Y be greater than or equal to 0?
1 answer
Last reply by: Dr Carleen Eaton
Sun Jan 27, 2013 12:51 PM
Post by Nathanael Shim on January 24, 2013
i am still a little confused by domain and range. could you explain to me again?
0 answers
Post by Aniket Dhawan on October 11, 2012
Great teaching,
this helped me a lot.
Thanks