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Similar Question 1
<p>Match each function with its equation on the next page. Then identify which function pairs are reciprocals.</p><p>a) <img src="/qimages/462" /></p><p>b) <img src="/qimages/463" /></p><p>c) <img src="/qimages/464" /></p><p>d) <img src="/qimages/465" /></p><p>e) <img src="/qimages/466" /></p><p>f) <img src="/qimages/467" /> </p><p>A) <code class='latex inline'>y= \displaystyle{\frac{1}{-(x-2)^2-1}}</code></p><p>B) <code class='latex inline'>y= \displaystyle{\frac{1}{x^2-1}}</code></p><p>C) <code class='latex inline'>y=\displaystyle{\frac{1}{2x-5}}</code></p><p>D) <code class='latex inline'>y=x^2-1</code></p><p>E) <code class='latex inline'>y=-(x-2)^2-1</code></p><p>F) <code class='latex inline'>y=2x-5</code></p>
Similar Question 2
<p>For the function, determine the domain and range, intercepts, positive/negative intervals, and increasing and decreasing intervals. Use this information to sketch a graph of the reciprocal function.</p><p><code class='latex inline'>\displaystyle f(x) = 2x^2 + 7x -4 </code></p>
Similar Question 3
<p>State the equation of the reciprocal of each function, and determine the equations of the vertical asymptotes of the reciprocal. </p><p><code class='latex inline'>f(x)=-3x+6</code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>State the domain and range of the reciprocal function.</p><p><code class='latex inline'>y=-\displaystyle{\frac{1}{2x-5}}</code></p>
<p>Sketch the graph of the reciprocal function.</p><p><code class='latex inline'>f(x)=x^2-6x</code></p>
<p>Sketch the graphs of the following reciprocal functions.</p><p><code class='latex inline'>y=\displaystyle{\frac{1}{2^x}}</code></p>
<p>State the equation of the reciprocal of each function, and determine the equations of the vertical asymptotes of the reciprocal. </p><p><code class='latex inline'>f(x)=x+5</code></p>
<p>For each function, determine the </p> <ul> <li>positive/negative intervals, and </li> <li>increasing/decreasing intervals.</li> </ul> <p><code class='latex inline'>f(x)=-2x^2+10x-12</code></p>
<p>State the equation of the reciprocal of each function, and determine the equations of the vertical asymptotes of the reciprocal. </p><p> <code class='latex inline'>f(x)=2x+5</code></p>
<p>A chemical company is testing the effectiveness of a new cleaning solution for killing bacteria. The test involves introducing the solution into a sample that contains approximately <code class='latex inline'>10 000</code> bacteria. The number of bacteria remaining, <code class='latex inline'>b(t)</code>, over time, <code class='latex inline'>t</code>, in seconds is given by the equation <code class='latex inline'>b(t)=10000\frac{1}{t}</code>.</p><p>How many bacteria will be left after 20 s?</p>
<p>Sketch.</p><p><code class='latex inline'>y=\displaystyle{\frac{1}{x^3}}</code></p>
<p>State the domain and range of the following: </p><p><code class='latex inline'>y=\displaystyle{\frac{1}{3x+4}}</code></p>
<p>For the function, determine the domain and range, intercepts, positive/negative intervals, and increasing and decreasing intervals. Use this information to sketch a graph of the reciprocal function.</p><p><code class='latex inline'>\displaystyle f(x) = 2x^2 + 7x -4 </code></p>
<p>Sketch the graph of the reciprocal of each function. </p><img src="/qimages/4242" />
<p>Sketch <code class='latex inline'>y=\displaystyle{\frac{1}{f(x)}}</code> for</p><p> <code class='latex inline'>f(x)=-(x+4)^2+1</code></p>
<p>Sketch the graph of the reciprocal of each function. </p><img src="/qimages/4248" />
<p>Match each function with its equation on the next page. Then identify which function pairs are reciprocals.</p><p>a) <img src="/qimages/462" /></p><p>b) <img src="/qimages/463" /></p><p>c) <img src="/qimages/464" /></p><p>d) <img src="/qimages/465" /></p><p>e) <img src="/qimages/466" /></p><p>f) <img src="/qimages/467" /> </p><p>A) <code class='latex inline'>y= \displaystyle{\frac{1}{-(x-2)^2-1}}</code></p><p>B) <code class='latex inline'>y= \displaystyle{\frac{1}{x^2-1}}</code></p><p>C) <code class='latex inline'>y=\displaystyle{\frac{1}{2x-5}}</code></p><p>D) <code class='latex inline'>y=x^2-1</code></p><p>E) <code class='latex inline'>y=-(x-2)^2-1</code></p><p>F) <code class='latex inline'>y=2x-5</code></p>
<p>State the equation of the reciprocal of each function, and determine the equations of the vertical asymptotes of the reciprocal. </p><p> <code class='latex inline'>f(x)=3x^2-4x-4</code></p>
<p>State the equation of the reciprocal of each function, and determine the equations of the vertical asymptotes of the reciprocal. </p><p><code class='latex inline'>f(x)=2x</code></p>
<p>A chemical company is testing the effectiveness of a new cleaning solution for killing bacteria. The test involves introducing the solution into a sample that contains approximately 10 000 bacteria. The number of bacteria remaining, <code class='latex inline'>b(t)</code>, over time, <code class='latex inline'>t</code>, in seconds is given by the equation <code class='latex inline'>b(t)=10000\frac{1}{t}</code>.</p><p> After how many seconds will only one bacterium be left?</p>
<p>Sketch the graph of the reciprocal of each function. </p><img src="/qimages/4247" />
<p>Sketch the graph of the reciprocal of each function. </p><img src="/qimages/469" />
<p>For each pair of functions, determine where the zeros of the original function occur and state the equations of the vertical asymptotes of the reciprocal function, if possible.</p><p><code class='latex inline'>f(x)=x-6, g(x)=\displaystyle{\frac{1}{x-6}}</code></p>
<p>An equation of the form <code class='latex inline'>y=\displaystyle{\frac{k}{x^2+bx+c}}</code> has a graph that closely matches the graph shown. Find the equation. </p><img src="/qimages/473" />
<p>Sketch <code class='latex inline'>y=\displaystyle{\frac{1}{f(x)}}</code> for</p><p><code class='latex inline'>f(x)=x^2-3x+2</code></p>
<p>State the equation of the reciprocal of each function, and determine the equations of the vertical asymptotes of the reciprocal. </p><p><code class='latex inline'>f(x)=-3x+6</code></p>
<p>Sketch.</p><p><code class='latex inline'>y=\displaystyle{\frac{1}{\sqrt{x}}}</code></p>
<p>For each pair of functions, determine where the zeros of the original function occur and state the equations of the vertical asymptotes of the reciprocal function, if possible.</p><p><code class='latex inline'>f(x)=4x^2-25, g(x)=\displaystyle{\frac{1}{4x^2-25}}</code></p>
<p>Sketch the graphs of the following reciprocal function.</p><p> <code class='latex inline'>y=\displaystyle{\frac{1}{\sin{x}}}</code></p>
<p>State the equation of the reciprocal of each function, and determine the equations of the vertical asymptotes of the reciprocal. </p><p><code class='latex inline'>f(x)=x-4</code></p>
<p>Sketch <code class='latex inline'>y=\displaystyle{\frac{1}{f(x)}}</code> for</p><p> <code class='latex inline'>f(x)=(x+3)^2</code></p>
<p>State the equation of the reciprocal of each function, and determine the equations of the vertical asymptotes of the reciprocal. </p><p><code class='latex inline'>f(x)=(x-3)^2</code></p>
<p>Determine the equation of the function in the graph shown.</p><img src="/qimages/474" />
<p>For each pair of functions, determine where the zeros of the original function occur and state the equations of the vertical asymptotes of the reciprocal function, if possible.</p><p><code class='latex inline'>f(x)=2x^2+5x+3, g(x)=\displaystyle{\frac{1}{2x^2+5x+3}}</code></p>
<p>Sketch <code class='latex inline'>y=\displaystyle{\frac{1}{f(x)}}</code> for</p><p> <code class='latex inline'>f(x)=x^2-4</code></p>
<p>Use your graphing calculator to explore and then describe the key characteristics of the family of reciprocal functions of the form <code class='latex inline'>g(x)=\displaystyle{\frac{1}{x+n}}</code>. </p><p>For the family of functions <code class='latex inline'>f(x)=x+n</code>, the y-intercept changes as the value of <code class='latex inline'>n</code> changes. Describe how the y-intercept changes and how this affects <code class='latex inline'>g(x)</code>.</p>
<p>Sketch <code class='latex inline'>y=\displaystyle{\frac{1}{f(x)}}</code> for</p><p><code class='latex inline'>f(x)=x^2+2</code></p>
<p>For each function, determine the </p> <ul> <li>positive/negative intervals, and </li> <li>increasing/decreasing intervals.</li> </ul> <p><code class='latex inline'>f(x)=x^2-x-12</code></p>
<p>State the domain and range of <code class='latex inline'>g(x)=\displaystyle{\frac{1}{x+n}}</code>.</p>
<p>Match function c) with its equation on the next page. Then identify which function pairs are reciprocals.</p><img src="/qimages/28114" /><img src="/qimages/28115" />
<p><strong>a)</strong> Find <code class='latex inline'>\frac{1}{f(2)}</code>, <code class='latex inline'>\frac{1}{f(4)}</code> and <code class='latex inline'>\frac{1}{f(6)}</code></p><img src="/qimages/468" /><p><strong>b)</strong> Find equations for<code class='latex inline'>y=\displaystyle{\frac{1}{f(x)}}</code>.</p>
<p>For the function, determine the domain and range, intercepts, positive/negative intervals, and increasing and decreasing intervals. Use this information to sketch a graph of the reciprocal function.</p><p><code class='latex inline'>f(x) = 3x + 2</code></p>
<p>For the function, determine the domain and range, intercepts, positive/negative intervals, and increasing and decreasing intervals. Use this information to sketch a graph of the reciprocal function.</p><p><code class='latex inline'>f(x) = 3x + 2</code></p>
<p>Sketch <code class='latex inline'>y=\displaystyle{\frac{1}{f(x)}}</code> for</p><p><code class='latex inline'>f(x)=(x-2)^2-3</code></p>
<p>For <code class='latex inline'>f(x) = x +n</code>, <code class='latex inline'>g(x)=\displaystyle{\frac{1}{x+n}}</code>, </p><p>at what point would the two graphs <code class='latex inline'>f(x)</code> and <code class='latex inline'>g(x)</code> intersect?</p>
<p>For each function, determine the </p> <ul> <li>positive/negative intervals, and </li> <li>increasing/decreasing intervals.</li> </ul> <p><code class='latex inline'>f(x)=-4x-3</code></p>
<p>A chemical company is testing the effectiveness of a new cleaning solution for killing bacteria. The test involves introducing the solution into a sample that contains approximately 10 000 bacteria. The number of bacteria remaining, <code class='latex inline'>b(t)</code>, over time, <code class='latex inline'>t</code>, in seconds is given by the equation <code class='latex inline'>b(t)=10000\frac{1}{t}</code>.</p><p>When is the model not accurate? Assume that the solution was introduced at <code class='latex inline'>t=0</code>.</p>
<p>A chemical company is testing the effectiveness of a new cleaning solution for killing bacteria. The test involves introducing the solution into a sample that contains approximately 10 000 bacteria. The number of bacteria remaining, <code class='latex inline'>b(t)</code>, over time, <code class='latex inline'>t</code>, in seconds is given by the equation <code class='latex inline'>b(t)=10000\frac{1}{t}</code>.</p><p>After how many seconds will only 5000 bacteria be left?</p>
<p>For each function, determine the </p> <ul> <li>positive/negative intervals, and </li> <li>increasing/decreasing intervals.</li> </ul> <p><code class='latex inline'>f(x)=\frac{1}{2x+8}</code></p>
<p>For each pair of functions, determine where the zeros of the original function occur and state the equations of the vertical asymptotes of the reciprocal function, if possible.</p><p><code class='latex inline'>f(x)=3x+4, g(x)=\displaystyle{\frac{1}{3x+4}}</code></p>
<p>State the equation of the reciprocal of each function, and determine the equations of the vertical asymptotes of the reciprocal. </p><p> <code class='latex inline'>f(x)=x^2-3x-10</code></p>
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