# Convert between Tables, Graphs, Mappings, and Lists of Points – Practice ProblemsHaving fun while studying, practice your skills by solving these exercises!

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A function is a particular kind of relation between sets. A function takes every element x in a starting set, called the domain, and tells us how to assign it to exactly one element y in an ending set, called the range. We can represent functions in different ways; let’s take a look at a few of them through the following example:

At a stationary supply store, one pen costs \$2.75. So the price the customer pays depends on how many pens they decide to buy. We can represent the amount the customer needs to pay with the function p(x)=2.75x. We have that the domain is the number of pens x the customer buys and the range is the amount the customer has to pay, 2.75x. Let’s look at some ways in which we can represent p(x):

One way of representing p(x) is via a mapping diagram. A mapping shows how the elements of the domain and range are paired. It’s a flow chart consisting of two parallel columns, showing the input x (first column) and output y (second column) values. Lines or arrows are drawn from domain to range, to represent the relation between any two elements. So for our example we would map 1 to 2.75, 2 to 5.50, 3 to 8.25, 4 to 11.00, 5 to 13.75, and so on.

We can also use tables, ordered pairs, and graphs to represent p(x). The easiest way to make a graph is to begin by making a table containing inputs and outputs. We would then call (x,p(x)) an ordered pair where x is the input and p(x) is the output. For our example, we can write the data from such a table as ordered pairs: (1, 2.75), (2, 5.50), (3, 8.25), (4,11.00), and (5,13.75). These ordered pairs can be plotted and lines can be drawn between them to get a graph.

Interpret functions that arise in applications in terms of the context.

CCSS.MATH.CONTENT.HSF.IF.B.4

Exercises in this Practice Problem
 Determine to which positions Emilia could have started. Explain how to represent the input and output of a function with a graph. Plot the given points in a graph. Decide which graph corresponds to which mapping diagram. Match the image with its corresponding definition. Determine the coordinates of the ordered pairs.