15. Q15
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Similar Question 1
<p>Use the degree and the sign of the leading coefficient to </p> <ul> <li><strong>i.</strong> describe the end behaviour of each polynomial function</li> <li><strong>ii.</strong> state which finite differences will be constant</li> <li><strong>iii.</strong> determine the value of the constant finite differences</li> </ul> <p><code class='latex inline'> \displaystyle p(x) = 0.6x^5 - 2x^4 + 8x </code></p>
Similar Question 2
<p>Consider the graph below.</p> <ul> <li>i. Does it represent a power function of even degree? odd degree? Explain.</li> <li>ii. State the sign of the leading coefficient. Justify your answer.</li> <li>iii. State the domain and range.</li> <li>iv. Identify any symmetry.</li> <li>v. Describe the end behaviour.</li> </ul> <img src="/qimages/98" />
Similar Question 3
<p> For the given pattern, find <code class='latex inline'>f(5)</code> and <code class='latex inline'>f(6)</code>. Also find the degree of <code class='latex inline'>f(n)</code>.</p><img src="/qimages/246" />
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>Consider the graph below.</p> <ul> <li>i. Does it represent a power function of even degree? odd degree? Explain.</li> <li>ii. State the sign of the leading coefficient. Justify your answer.</li> <li>iii. State the domain and range.</li> <li>iv. Identify any symmetry.</li> <li>v. Describe the end behaviour.</li> </ul> <img src="/qimages/98" />
<p>Use the degree and the sign of the leading coefficient to </p> <ul> <li><strong>i.</strong> describe the end behaviour of each polynomial function</li> <li><strong>ii.</strong> state which finite differences will be constant</li> <li><strong>iii.</strong> determine the value of the constant finite differences</li> </ul> <p><code class='latex inline'> \displaystyle p(x) = 0.6x^5 - 2x^4 + 8x </code></p>
<p>Each graph represents a polynomial function of degree 3, 4, 5, or 6. Determine the least possible degree of the function corresponding to each graph. Justify your answer.</p><img src="/qimages/169" />
<p>Use the degree and the sign of the leading coefficient to </p> <ul> <li><strong>i.</strong> describe the end behaviour of each polynomial function</li> <li><strong>ii.</strong> state which finite differences will be constant</li> <li><strong>iii.</strong> determine the value of the constant finite differences</li> </ul> <p><code class='latex inline'> \displaystyle f(x) = 3 -x </code></p>
<p>The following polynomial equation has no real solutions:</p><p><code class='latex inline'>0=5x^8+10x^6+7x^4+18x^2+132</code></p><p>Why?</p>
<p>Consider the graph below.</p> <ul> <li>i. Does it represent a power function of even degree? odd degree? Explain.</li> <li>ii. State the sign of the leading coefficient. Justify your answer.</li> <li>iii. State the domain and range.</li> <li>iv. Identify any symmetry.</li> <li>v. Describe the end behaviour.</li> </ul> <img src="/qimages/97" />
<p>Consider the graph below.</p><p><strong>i.</strong> Does it represent a power function of even degree? odd degree? Explain.</p><p><strong>ii.</strong> State the sign of the leading coefficient. Justify your answer.</p><p><strong>iii.</strong> State the domain and range.</p><p><strong>iv.</strong> Identify any symmetry.</p><p><strong>v.</strong> Describe the end behaviour.</p><img src="/qimages/99" />
<p>Each graph represents a polynomial function of degree 3, 4, 5, or 6. Determine the least possible degree of the function corresponding to each graph. Justify your answer.</p><img src="/qimages/168" />
<p>Consider the graph below.</p><p><strong>i.</strong> Does it represent a power function of even degree? odd degree? Explain.</p><p><strong>ii.</strong> State the sign of the leading coefficient. Justify your answer.</p><p><strong>iii.</strong> State the domain and range.</p><p><strong>iv.</strong> Identify any symmetry.</p><p><strong>v.</strong> Describe the end behaviour.</p><img src="/qimages/96" />
<p> For the given pattern, find <code class='latex inline'>f(5)</code> and <code class='latex inline'>f(6)</code>. Also find the degree of <code class='latex inline'>f(n)</code>.</p><img src="/qimages/246" />
<p>Use the degree and the sign of the leading coefficient to </p> <ul> <li><strong>i.</strong> describe the end behaviour of each polynomial function</li> <li><strong>ii.</strong> state which finite differences will be constant</li> <li><strong>iii.</strong> determine the value of the constant finite differences</li> </ul> <p><code class='latex inline'> \displaystyle f(x) = -4x^3 + 2x^2 -x + 5 </code></p>
<p>Consider the function <code class='latex inline'>f(x) = x^3 + 2x^2 -5x -6</code>.</p><p>a) How do the degree and the sign of the leading coefficient correspond to the end behaviour of the polynomial function?</p><p>b) Sketch a graph of the polynomial function.</p><p>c) What can you tell about the value of the third differences for this function?</p>
<p>i. State the degree of the polynomial function that corresponds to each constant finite difference. </p><p>ii. Determine the value of the leading coefficient for each polynomial function.</p><p>fifth differences = 60</p>
<p>Use the degree and the sign of the leading coefficient to </p> <ul> <li><strong>i.</strong> describe the end behaviour of each polynomial function</li> <li><strong>ii.</strong> state which finite differences will be constant</li> <li><strong>iii.</strong> determine the value of the constant finite differences</li> </ul> <p><code class='latex inline'> \displaystyle h(x) = -x^6 + 8x^3 </code></p>
<p>Each graph represents a polynomial function of degree <code class='latex inline'>3, 4, 5</code>, or <code class='latex inline'>6</code>. Determine the least possible degree of the function corresponding to each graph. Justify your answer.</p><img src="/qimages/166" />
<p>Use the degree and the sign of the leading coefficient to </p> <ul> <li><strong>i.</strong> describe the end behaviour of each polynomial function</li> <li><strong>ii.</strong> state which finite differences will be constant</li> <li><strong>iii.</strong> determine the value of the constant finite differences</li> </ul> <p><code class='latex inline'> \displaystyle f(x) = x^2 + 3x - 1 </code></p>
<p>For the graph below</p> <ul> <li>State the sign of the leading coefficient. Justify your answer.</li> <li>Describe the end behaviour.</li> <li>Identify any symmetry.</li> <li>State the number of minimum and maximum points and local minimum and local maximum points. How are these related to the degree of the function?</li> </ul> <img src="/qimages/4607" />
<p>Use the degree and the sign of the leading coefficient to </p> <ul> <li><strong>i.</strong> describe the end behaviour of each polynomial function</li> <li><strong>ii.</strong> state which finite differences will be constant</li> <li><strong>iii.</strong> determine the value of the constant finite differences</li> </ul> <p><code class='latex inline'> \displaystyle h(x) = -7x^4 + 2x^3 -3x^2 +4 </code></p>
<p> What is the degree of a polynomial <code class='latex inline'>y = P(x)</code> if the y-values are all equal for the <code class='latex inline'>11^{th}</code> set of differences of consecutive x-values, are not equal for the 10th set of differences?</p>
<p>i. State the degree of the polynomial function that corresponds to each constant finite difference. </p><p>ii. Determine the value of the leading coefficient for each polynomial function.</p><p>third differences = <code class='latex inline'>36</code></p>
<p><code class='latex inline'>\displaystyle \begin{array}{ccc} & y = -x^3 & y = \frac{3}{7}x^2 & y = 5x \\ & y = 4x^5 & y = -x^6 & y = -0.1x^{11} \\ & y = 2x^4 & y = -9x^{10} \\ \end{array} </code></p><p>Categorize end behaviour of power functions above below:</p><p>Quadrant III <code class='latex inline'>\to</code> Quadrant I: </p><p>Quadrant II <code class='latex inline'>\to</code> Quadrant IV: </p><p>Quadrant II <code class='latex inline'>\to</code> Quadrant I: </p><p>Quadrant III <code class='latex inline'>\to</code> Quadrant IV: </p>
<p>Each graph represents a polynomial function of degree 3, 4, 5, or 6. Determine the least possible degree of the function corresponding to each graph. Justify your answer.</p><img src="/qimages/167" />
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