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<h4>Identifying if a Relationship Is a Function</h4>
<p>A function is a relation in which each possible input value leads to exactly one output value. We say “the
output is a function of the input.”</p>
<div class="os-raise-graybox">
<p class="os-raise-text-bold">How to determine if a relationship is a function.</p>
<ol class="os-raise-noindent">
<li>Identify the input values.</li>
<li>Identify the output values.</li>
<li>If each input value leads to only one output value, classify the relationship as a function. If any input value
leads to two or more outputs, do not classify the relationship as a function.</li>
</ol>
</div>
<br><p class="os-raise-text-bold">Example 1
</p>
<p>The coffee shop menu, shown below, consists of items and their prices.</p>
<p><img
alt="A menu of donut prices from a coffee shop where a plain donut is $1.49 and a jelly donut and chocolate donut are $1.99."
class="img-fluid atto_image_button_text-bottom" height="168"
src="https://k12.openstax.org/contents/raise/resources/891ac2bd18a398c550f2aae376fe76fe5b13d4d4" width="349"></p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="2b451c86-005c-4153-a66b-22ef892a6cb8"
data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" type="a">
<li>Is price a function of the item?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Let’s begin by considering the input values as the items on the menu. The output values are then the
prices. Each item on the menu has only one price, so the price is a function of the item.</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="beb3230c-060b-4d6d-b9b0-f0199ff759ae"
data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2" type="a">
<li>Is the item a function of the price?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Two items on the menu have the same price. If we consider the prices to be the input values and the items to be
the output, then the same input value could have more than one output associated with it. See the image below.
Therefore, the item is a not a function of price.</p>
<p><img alt="Association of the prices to the donuts." class="img-fluid atto_image_button_text-bottom" height="168"
src="https://k12.openstax.org/contents/raise/resources/4ca8a33070cb29d5a0d84af71c52fecedce72117" width="349">
</p>
</div>
</div>
<!--Interaction End -->
<br>
<p><strong>Example 2</strong></p>
<p>In a particular math class, the overall percent grade corresponds to a grade point average. Is grade point average a
function of the percent grade? Is the percent grade a function of the grade point average? The table below shows a possible
rule for assigning grade points.</p>
<br>
<table class="os-raise-horizontaltable">
<thead></thead>
<tbody>
<tr>
<th scope="row">Percent grade</th>
<td>
0–56
</td>
<td>
57–61
</td>
<td>
62–66
</td>
<td>
67–71
</td>
<td>
72–77
</td>
<td>
78–86
</td>
<td>
87–91
</td>
<td>
92–100
</td>
</tr>
<tr>
<th scope="row">Grade point average</th>
<td>
0.0
</td>
<td>
1.0
</td>
<td>
1.5
</td>
<td>
2.0
</td>
<td>
2.5
</td>
<td>
3.0
</td>
<td>
3.5
</td>
<td>
4.0
</td>
</tr>
</tbody>
</table>
<br>
<h5>Solution</h5>
<p>For any percent grade earned, there is an associated grade point average, so the grade point average is a function of
the percent grade. In other words, if we input the percent grade, the output is a specific grade point average.</p>
<p>In the grading system given, there is a range of percent grades that correspond to the same grade point average. For
example, students who receive a grade point average of 3.0 could have a variety of percent grades, ranging from 78 all
the way to 86. Thus, percent grade is not a function of grade point average.</p>
<h4>Try It: Identifying if a Relationship Is a Function</h4>
<p>The table below lists the five greatest baseball players of all time in order of rank.</p>
<br>
<table class="os-raise-midsizetable">
<thead>
<tr>
<th scope="col">Player</th>
<th scope="col">Rank</th>
</tr>
</thead>
<tbody>
<tr>
<td>
Babe Ruth
</td>
<td>
1
</td>
</tr>
<tr>
<td>
Willie Mays
</td>
<td>
2
</td>
</tr>
<tr>
<td>
Ty Cobb
</td>
<td>
3
</td>
</tr>
<tr>
<td>
Walter
Johnson
</td>
<td>
4
</td>
</tr>
<tr>
<td>
Hank Aaron
</td>
<td>
5
</td>
</tr>
</tbody>
</table>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<br>
<ol class="os-raise-noindent" type="a">
<li>Is the rank a function of the player name?</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer. Then select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answers:</p>
<p>Here is how to determine which variable is a function of the other:</p>
<p>Identify the input and output.</p>
<p>Since the name is the input and the rank is the output, the rank is a function of the player name.</p>
<br>
</div>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<br>
<ol class="os-raise-noindent" type="a" start="2">
<li>Is the player name a function of the rank?</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer. Then select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answers:</p>
<p>Here is how to determine which variable is a function of the other:</p>
<p>Identify the input and output.</p>
<p>Since the rank is the input and the name is the output, the player name is a function of the rank.</p>
<br>
</div>