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<h4>Graphing Situations as Functions</h4>
<p>Example 1:</p>
<p>Draw a graph representing a function that describes Sam’s distance from home over an hour.</p>
<p>A: Sam rides his bike to his friend’s house at a constant rate for 20 minutes.<br>
B: Sam plays for 20 minutes at his friend’s house.<br>
C: Sam and his friend bike together to an ice cream shop that is between their houses for 20 minutes.</p>
<p>Here is a sample graph. Notice that the \(x\)-axis is labeled “time in minutes” and the \(y\)-axis is labeled “distance from home (miles).”</p>
<p>The distance from home is increasing as Sam rides to his friend’s house. While playing at his friend’s house, the distance remained constant and unchanged. When Sam left his friend’s house for the ice cream shop, the distance from home decreased because the shop is in between their houses, so Sam was getting closer to home.</p>
<p><img alt="GRAPH THAT SHOWS DISTANCE FROM HOME IN MILES AS A FUNCTION OF TIME IN MINUTES. X-AXIS GOES FROM 0 TO 60 IN INCREMENTS OF 10. Y-AXIS GOES FROM 0 TO 3.5 IN INCREMENTS OF 0.5. THE GRAPH INCREASES LINEARLY FROM X = 0 TO X = 20, REACHING A DISTANCE OF 3.25 MILES (SECTION A), REMAINS CONSTANT FROM X = 20 TO X = 40 (SECTION B), AND THEN DECREASES (SECTION C)." class="img-fluid atto_image_button_text-bottom" height="286" src="https://k12.openstax.org/contents/raise/resources/270cc818f622d4b3644527d27a8807e4e94fcbbf" width="300"></p>
<p>Example 2:</p>
<p>Tyler filled up his bathtub, took a bath, and then drained the tub. The function gives the depth of the water \(B\), in inches, \(t\) minutes after Tyler began to fill the bathtub.</p>
<p><img alt="Blank coordinate plane, no grid, origin O. Horizontal axis, time, minutes, from 0 to 40 by 10’s. Vertical axis, depth, inches, from 0 to 15 by 5’s." class="img-fluid atto_image_button_text-bottom" height="228" src="https://k12.openstax.org/contents/raise/resources/0da028a19bba61dc0287d112e3f1bcaa82e751ed" width="307"></p>
<p>These statements describe how the water level in the tub was changing over time. Use the statements to sketch an approximate graph of the function.</p>
<ul>
<li>\(B(0) = 0\)</li>
<li>\(B(1) < B(7)\)</li>
<li>\(B(9) = 11\)</li>
<li>\(B(10) = B(20)\)</li>
<li>\(B(20) > B(40)\)</li>
</ul>
<p>A sample graph below meets all of the statements above.</p>
<p><img src="https://k12.openstax.org/contents/raise/resources/b68a468b76a04fd72a662b975eeddc163e5e3622" width="300"></p>
<h4>Try It: Graphing Situations as Functions</h4>
<p>A rock climber begins her descent from a height of 50 feet. She slowly descends at a constant rate for 4 minutes. She takes a break for 1 minute; she then realizes she left some of her gear on top of the rock and climbs more quickly back to the top at a constant rate.</p>
<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">
<p>Create a graph representing this situation.</p>
</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>Here is how to graph the situation:</p>
<p><img alt="GRAPH THAT SHOWS HEIGHT ABOVE THE GROUND IN FEET AS A FUNCTION OF TIME IN MINUTES. X-AXIS GOES FROM 0 TO 10 IN INCREMENTS OF 2. Y-AXIS GOES FROM 0 TO 50 IN INCREMENTS OF 10. THE GRAPH DECREASES LINEARLY FROM X = 0 TO X = 4, REMAINS CONSTANT FROM X = 4 TO X = 5, AND THEN INCREASES LINEARLY WITH A STEEPER SLOPE." class="atto_image_button_text-bottom" height="286" src="https://k12.openstax.org/contents/raise/resources/c7da6d46611768a9a4ca95bde74f8c161b357bce" width="300"></p>
</div>