Let’s Think About It
It is Reggie’s first day on the job at The Taco Shop near his house. Reggie is looking over the menu when he notices that the restaurant now offers family or group combo orders of 12 tacos. If a customer orders 1 combo, he will get 12 tacos. If the customer orders 2 combos, he will get 24 tacos. Because his math class recently studied functions, Reggie realizes the number of tacos is a function of the number of combos ordered, as demonstrated below.
How can this data can be displayed visually with a graph?
In this concept, you will learn how to graph linear functions.
A function is a set of data that has a specific relationship. One variable in the data set is related to or depends on a different variable in the same data set. Each input matches with only one output.
Take a look at the following table.
Here is another table.
Let’s look at functions in a real life situation.
Felix has a job cutting grass in the summer time. He earns $10.00 per lawn that he cuts. The amount of money that Felix makes is related to the number of lawns that he cuts. Let’s look at some data about Felix and then show how this forms a function.
Felix cut the following lawns on four different days.
This is represented in the following table.
You can say that the amount of money that Felix earns is a function of the number of lawns that he mows.
You can also graph functions on the coordinate grid by using the values in each column to form ordered pairs.
Now you can graph the data.
This graph forms a linear function. Anytime a graph forms a line like this, it is called a graph of a linear function. If the line rises from left to right, the graph of the function increases. If the line slopes downward from left to right, the graph of the linear function decreases.
On a coordinate plane, graph the linear function that is represented by the ordered pairs in the table below.
Then connect them as shown below.
Notice that the graph of this function is a straight line that decreases from left to right. That is because this function is a linear function.
Answer the following questions about graphs and linear functions.
Does this graph show an increase or a decrease?
First, look at the line representing this function. The line rises as it goes from left to right. Therefore, the function increases.
The answer is the function increases.
According to the graph in Example 1, what is the largest number of wind chimes sold?
The answer is 5 wind chimes.
Remember Reggie and his first day at The Taco Shop?
A customer walks up to the counter and asks Reggie how many tacos come in the family combo. Reggie tells the customer that each combo contains 12 tacos. The customer tells Reggie that he needs to order enough tacos for 11 people. He tells Reggie that 5 tacos should be enough for each person, which means he needs to get at least 55 tacos. Reggie does the math in his head and figures out that 5 combo packs will be 60 tacos because the number of tacos is a function of the number of combos the man orders. Reggie walks over to the kitchen and tells the cooks to get busy.
The following chart represents this function.
How can Reggie display this function and data on a graph?
To graph this linear function, first identify the ordered pairs.
Here is a graph representing the data from the table.
Notice that this is a linear graph showing the relationship between number of combo packs and the number of tacos.
Graph each function represented by the data in the table then determine which represent linear graphs and which ones do not.