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	<id>https://gradwiki.math.ucr.edu/index.php?action=history&amp;feed=atom&amp;title=005_Sample_Final_A%2C_Question_18</id>
	<title>005 Sample Final A, Question 18 - Revision history</title>
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	<updated>2026-04-05T19:14:05Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://gradwiki.math.ucr.edu/index.php?title=005_Sample_Final_A,_Question_18&amp;diff=627&amp;oldid=prev</id>
		<title>Matt Lee: Created page with &quot;''' Question ''' Graph the following function, &lt;center&gt;&lt;math&gt;f(x) = \left(\frac{1}{3}\right)^{x+1} + 1&lt;/math&gt;&lt;/center&gt; &lt;br&gt; Make sure to label any asymptotes, and at least two...&quot;</title>
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		<updated>2015-05-01T04:16:42Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;&amp;#039;&amp;#039;&amp;#039; Question &amp;#039;&amp;#039;&amp;#039; Graph the following function, &amp;lt;center&amp;gt;&amp;lt;math&amp;gt;f(x) = \left(\frac{1}{3}\right)^{x+1} + 1&amp;lt;/math&amp;gt;&amp;lt;/center&amp;gt; &amp;lt;br&amp;gt; Make sure to label any asymptotes, and at least two...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;''' Question ''' Graph the following function, &amp;lt;center&amp;gt;&amp;lt;math&amp;gt;f(x) = \left(\frac{1}{3}\right)^{x+1} + 1&amp;lt;/math&amp;gt;&amp;lt;/center&amp;gt; &amp;lt;br&amp;gt;&lt;br /&gt;
Make sure to label any asymptotes, and at least two points on the graph.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible mw-collapsed&amp;quot; style = &amp;quot;text-align:left;&amp;quot;&lt;br /&gt;
! Final Answers&lt;br /&gt;
|-&lt;br /&gt;
|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, &amp;lt;math&amp;gt;a_n = (-a)^n&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.&lt;br /&gt;
|-&lt;br /&gt;
|c) False. &amp;lt;math&amp;gt;y = x^2&amp;lt;/math&amp;gt; does not have an inverse.&lt;br /&gt;
|-&lt;br /&gt;
|d) True. &amp;lt;math&amp;gt;cos^2(x) - cos(x) = 0&amp;lt;/math&amp;gt; has multiple solutions.&lt;br /&gt;
|-&lt;br /&gt;
|e) True.&lt;br /&gt;
|-&lt;br /&gt;
|f) False. &lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>Matt Lee</name></author>
	</entry>
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