Convert between Tables, Graphs, Mappings, and Lists of Points – Practice Problems

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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.


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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.