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siwelwerd merged 3 commits into from
Jan 20, 2025
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additions to FN1 #516

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5f33e4b
additions to FN1
AbbyANoble Dec 19, 2024
c136b49
Update source/precalculus/source/02-FN/01.ptx
AbbyANoble Jan 20, 2025
840c708
Merge branch 'main' into FN1-additions
siwelwerd Jan 20, 2025
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181 changes: 176 additions & 5 deletions source/precalculus/source/02-FN/01.ptx
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Expand Up @@ -152,11 +152,176 @@
</task>
</activity>

<remark>
<p>
Notice that in <xref ref="FN1-exploring-relations-1"/>, <xref ref="FN1-exploring-relations-2"/>, and <xref ref="FN1-exploring-relations-3"/>, each set represents a very different relationship. Many concepts in mathematics will depend on particular relationships, so it is important to be able to visualize relationships and compare them.
</p>
</remark>
<activity xml:id="FN1-exploring-relations-4">
<introduction>
<p>
Use mapping notation to create a visual representation of the following relation.
<me>(3,-2), (-4,-1), (3,5)</me>
</p>
</introduction>
<task>
<statement>
<p>
What is the domain?
<ol marker= "A." cols="1">
<li> {<m>-4,-2,-1,3,5</m>} </li>
<li> {<m>-4,3</m>}</li>
<li> {<m>-2,-1,5</m>} </li>
<li> {<m>-4,3,3</m>} </li></ol></p>
</statement>
<answer>
<p>
B
</p>
</answer>
</task>
<task>
<statement>
<p>
What is the range?
<ol marker= "A." cols="1">
<li> {<m>-4,-2,-1,3,5</m>} </li>
<li> {<m>-4,3</m>}</li>
<li> {<m>-2,-1,5</m>} </li>
<li> {<m>-4,3,3</m>} </li></ol></p>
</statement>
<answer>
<p>
C
</p>
</answer>
</task>

</activity>



<activity xml:id="FN1-exploring-relations-summary">
<statement>
<p>
Now that you have created a visual representation for each of <xref ref="FN1-exploring-relations-1"/>, <xref ref="FN1-exploring-relations-2"/>, <xref ref="FN1-exploring-relations-3"/>, and <xref ref="FN1-exploring-relations-4"/>, what similarities do you see? What differences?
</p>
</statement>
<answer>
<p>
Students may mention that some have repeated <m>x</m>-values, some have repeated <m>y</m>-values, and some don't.
</p>
</answer>
</activity>

<activity xml:id="FN1-menu-as-function">
<introduction>
<p>
Consider the menus shown below for two different fast food restaurants. We'll consider the Items as inputs (<m>x</m>-values) and the Cost as outputs (<m>y</m>-values).
<sidebyside>
<tabular>
<row header="yes" bottom="minor" >
<cell>McRonald's Item</cell>
<cell>Cost</cell>
</row>
<row halign="center">
<cell>Nuggets</cell>FN1-menu-as-function
<cell><m>\$5</m></cell>
</row>
<row halign="center">
<cell>Burger</cell>
<cell><m>\$6</m></cell>
</row>
<row halign="center">
<cell>Fries</cell>
<cell><m>\$3</m></cell>
</row>
<row halign="center">
<cell>Nachos</cell>
<cell><m>\$6</m></cell>
</row>
</tabular>
<tabular>
<row header="yes" bottom="minor" >
<cell>Burger Queen's Item</cell>
<cell>Cost</cell>
</row>
<row halign="center">
<cell>Nuggets</cell>
<cell><m>\$4</m></cell>
</row>
<row halign="center">
<cell>Burger</cell>
<cell><m>\$8</m></cell>
</row>
<row halign="center">
<cell>Fries</cell>
<cell><m>\$2</m></cell>
</row>
<row halign="center">
<cell>Nuggets</cell>
<cell><m>\$7</m></cell>
</row>
</tabular>
</sidebyside>
</p>
</introduction>
<task>
<statement>
<p>
How much would it cost to get nuggets and fries at McRonald's?
<ol marker= "A." cols="4">
<li> <m>\$8</m> </li>
<li> <m>\$9</m> </li>
<li> <m>\$11</m> </li>
<li> <m>\$12</m> </li>
</ol>
</p>
</statement>
<answer>
<p>
A
</p>
</answer>
</task>
<task>
<statement>
<p>
How much would it cost to get nuggets and fries at Burger Queen?
<ol marker= "A." cols="4">
<li> <m>\$6</m> </li>
<li> <m>\$9</m> </li>
<li> <m>\$10</m> </li>
<li> <m>\$12</m> </li>
</ol>
</p>
</statement>
<answer>
<p>
A, B, or not able to be determined. Notice that that menu is not a function since nuggets are a repeated item.
</p>
</answer>
</task>
<task>
<statement>
<p>
Notice that burgers and nachos cost the same amount at McRonald's. Is that an issue? Explain your reasoning.
</p>
</statement>
<answer>
<p>
No. It's okay for two items to have the same price.
</p>
</answer>
</task>
<task>
<statement>
<p>
Notice on the Burger Queen menu that nuggets cost <m>\$4</m> in one spot but <m>\$7</m> in another spot. Is that an issue? Explain your reasoning.
</p>
</statement>
<answer>
<p>
Yes. It's not clear how much nuggets cost.
</p>
</answer>
</task>
</activity>

<definition xml:id="def-function">
<statement>
Expand All @@ -168,6 +333,12 @@
</statement>
</definition>

<remark>
<p>
We see that in <xref ref="FN1-menu-as-function"/>, the McRonald's menu is a function. There is no confusion in determining the cost of a given menu item. However, Burger Queen's menu is not a function. There is a discrepancy in the cost of nuggets, and the menu could cause confusion.
</p>
</remark>

<activity xml:id="FN1-determine-if-a-function">
<introduction>
<p>
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