# Using Tables and Graphs in the Real World

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• 0:05 Tables
• 1:02 Tables in the Real World
• 3:41 Graphs
• 4:17 Graphs in the Real World
• 5:10 Lesson Summary

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

We use tables and graphs in algebra as ways to visually show an equation or function. But do we really use these in the real world? Is it that important to learn about tables and graphs? Find out in this video lesson.

## Tables

Stop picturing tables with food on top. That's not the kind of table we're talking about here. The tables we are talking about are the ones you create or read with rows and columns of data. In math, you use tables to help you keep track of points for a function so you can plot the points later. For example, for the function y = x^2, we have a table like this:

x y
1 1
2 4
3 9

How did we get the information in the table from the function? We first decided to pick our x values of 1, 2, and 3. We then plugged in each of our x values into our function to evaluate it at that number to get our y value. We make three evaluations since we have three different x values. The more numbers we have in our table, the more accurate our table will be at representing our function. So, instead of having a multiplication table, you now have a function table.

## Tables in the Real World

So, what about in the real world? Are tables that useful in the real world to make them worth learning about and remembering? Yes, indeed they are!

If you keep your eyes and mind open, you will spot so many uses of tables in the real world. Many useful real-world tables also represent functions. But, since it's easier to grasp information from a table than it is by looking at a function, you will see a table instead of a function.

For example, think about cell phones for a minute. With most cell phone plans, you are given so many free minutes per month and then you have to pay for every minute you talk if you go over your free minutes. Your cell phone company usually represents this information in the form of a table. If you visit their website, you will see this table of information. But did you know that there is a formula behind this? Say, for example, we see a table like this one:

Plan Free Minutes Monthly Cost Overage
A 450 \$49.99 40 cents per minute
B 700 \$89.99 30 cents per minute
C 1400 \$129.99 20 cents per minute

Look at plan A. It looks pretty decent. You pay \$49.99 for 450 free minutes every month and if you happen to talk more than 450 minutes, you only pay .40 cents a minute. You're probably thinking, 'how is this a function?' Let me show you.

\$49.99 is our monthly cost for the first 450 minutes, so we have the function y = 49.99, where y is our monthly bill amount for the first 450 minutes or when x is less than 450. The .40 cents per minute is paid only when we go over 450 minutes. How will this be included?

We need to have another equation for minutes beyond 450. If x is our time on the phone, I have to somehow deduct 450 minutes from it before multiplying it by .40 cents. I can do that by subtracting 450 first from x and then multiplying by 0.40. I then need to add this amount to my \$49.99 per month.

So, my equation for minutes beyond 450 will look like y = 49.99 + 0.40(x - 450). I actually have two functions, one is for minutes up to 450 minutes and another for minutes beyond 450 minutes, behind the table of information that looks so simple and is so easy to understand. Keep your eyes open and you will find even more examples of tables in the real world.

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