Start by identifying the radius and area coordinates on the axes. Then, we will trace along the grid lines to the point on which both coordinates lie.
B
A relation is a function when each input is assigned to exactly one output.
A
B
Yes, see solution.
Practice makes perfect
We are told that Hannah approximates the areas of circles and records her data in a table.
Radius (in.)
1
2
3
4
5
Area (in^2)
3
12
27
48
75
We are asked to graph all the ordered pairs. We can begin by graphing just one, let's say that we want to graph the fourth ordered pair. The fourth ordered pair has the radius r equal to 4 inches and the area A is 48 inches squared.
Radius (in.)
1
2
3
4
5
Area (in^2)
3
12
27
48
75
We will start by identifying the r- and A-coordinates on the axes. Then, we will trace along the grid lines to the point on which both coordinates lie. Let's do this for the fourth ordered pair from the table, (4,48).
Now, we will repeat this for the other ordered pairs from the table.
We are asked whether the relation represented in the table is a function. Let's recall when a relation becomes a function.
When Is a Relation Also a Function?
A relation is a function when each input is assigned to exactly one output.
To determine if each input of the relation is assigned to exactly one output, we can look at the graph that we made in the previous part.
In this relation, the input is a radius and the output is the corresponding area of a circle. From the graph, we can see that each radius is assigned to exactly one area. Therefore, this relation is a function.
