15. Q15
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Similar Question 1
<ul> <li>i. Determine whether each function even, odd, or neither. Explain.</li> <li>ii. Without graphing, determine if each polynomial function has line symmetry about the y-axis. point symmetry about the origin, or neither. Explain.</li> </ul> <p><code class='latex inline'>y = -2x^6 + x^4 + 8</code></p>
Similar Question 2
<ul> <li>i. Determine whether each function even, odd, or neither. Explain.</li> <li>ii. Without graphing, determine if each polynomial function has line symmetry about the y-axis. point symmetry about the origin, or neither. Explain.</li> </ul> <p><code class='latex inline'>y = -2x^6 + x^4 + 8</code></p>
Similar Question 3
<p> Determine whether each graph represents an even-degree or an odd-degree polynomial function. Explain your reasoning.</p><img src="/qimages/297" />
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>Describe the similarities and differences between the line <code class='latex inline'>y = x</code> and power functions with odd degree greater than one. Use graphs to support your answer.</p>
<ul> <li>i. Determine whether each function even, odd, or neither. Explain.</li> <li>ii. Without graphing, determine if each polynomial function has line symmetry about the y-axis. point symmetry about the origin, or neither. Explain.</li> </ul> <p><code class='latex inline'>y= -2x^3+ 5x</code></p>
<p>Given <code class='latex inline'>f(x) = ax^7 + bx^3 + cx - 5</code>, where <code class='latex inline'>a, b</code>, and <code class='latex inline'>c</code> are constants, if <code class='latex inline'>f(-1) = 7</code> then determine the value of <code class='latex inline'>f(1)</code>.</p>
<p>A function is said to be even if <code class='latex inline'>f(-x) = f(x)</code> for all values of . A function is said to be odd if <code class='latex inline'>f(-x) = -f(x)</code> for all values of <code class='latex inline'>x</code>.</p><p>Is the function <code class='latex inline'>y = \cos x</code> even, odd, or neither?</p>
<ul> <li>i. Determine whether each function even, odd, or neither. Explain.</li> <li>ii. Without graphing, determine if each polynomial function has line symmetry about the y-axis. point symmetry about the origin, or neither. Explain.</li> </ul> <p><code class='latex inline'>y=x^4 -x^2</code></p>
<p>For the graphs below</p> <ul> <li>(a) State the least possible degree.</li> <li>(b) State the sign of the leading coefficient.</li> <li>(c) Describe the end behaviour of the graph.</li> <li>(d) Identify the type of symmetry, if it exists.</li> </ul> <img src="/qimages/296" />
<p> Determine whether each graph represents an even-degree or an odd-degree polynomial function. Explain your reasoning.</p><img src="/qimages/298" />
<p>Explain algebraically why a polynomial that is an odd function, say <code class='latex inline'>f(x)</code> is no longer an odd function when a nonzero constant is added.</p>
<p>Given the function <code class='latex inline'>f(x) = x^3 - 2x</code>, sketch <code class='latex inline'>y = f(|x|)</code>.</p>
<ul> <li>i. Determine whether each function even, odd, or neither. Explain.</li> <li>ii. Without graphing, determine if each polynomial function has line symmetry about the y-axis. point symmetry about the origin, or neither. Explain.</li> </ul> <p><code class='latex inline'>y= -4x^5+ 2x^2</code></p>
<p> Determine whether each graph represents an even-degree or an odd-degree polynomial function. Explain your reasoning.</p><img src="/qimages/296" />
<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>Determine, algebraically, whether each function has point symmetry about the origin or line symmetry about the y-axis. State whether each function is even, odd, or neither. Show your work.</p><p> <code class='latex inline'>p(x) = -(x + 5)^2(x -5)^3</code></p>
<p>Without graphing, determine if each polynomial function has line symmetry, point symmetry or neither. </p><p><code class='latex inline'> \displaystyle g(x) = -7x^6 +3x^4 + 6x^2 </code></p>
<p> Determine whether each graph represents an even-degree or an odd-degree polynomial function. Explain your reasoning.</p><img src="/qimages/295" />
<p>Determine an even function equation for a function with x-intercepts at <code class='latex inline'>\frac{2}{3}</code> and <code class='latex inline'>5</code>, passing through the point <code class='latex inline'>(-1, -96)</code></p>
<p>Write equations for two even functions with four x-intercepts, two of which are <code class='latex inline'>\frac{2}{3}</code> and 5.</p>
<p>Determine if the function is even or odd or neither</p><p><code class='latex inline'> \displaystyle P(x) = 3x^4 - 2x^2 </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/166" />
<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>For the graphs below</p> <ul> <li>(a) State the least possible degree.</li> <li>(b) State the sign of the leading coefficient.</li> <li>(c) Describe the end behaviour of the graph.</li> <li>(d) Identify the type of symmetry, if it exists.</li> </ul> <img src="/qimages/295" />
<p>Determine an equation for a function with <code class='latex inline'>x</code>-intercepts at <code class='latex inline'>\frac{2}{3}</code>, 5 and passing through the point <code class='latex inline'>(-1, -96)</code> and reflected on the <code class='latex inline'>x</code>-axis.</p>
<p>Show that the function is even or odd or neither.</p><p><code class='latex inline'> f(x) = \frac{x^3}{|x|} + x^2 </code></p>
<p>Without graphing, determine if each polynomial function has line symmetry, point symmetry or neither. </p><p><code class='latex inline'> \displaystyle h(x) = x^3 -3x^2 + 5x </code></p>
<p> Graph each pair of functions. What do you notice? Provide an algebraic explanation for what you observe.</p><p>i. <code class='latex inline'>y =(-x)^2</code> and <code class='latex inline'>y = x^2</code></p><p>ii. <code class='latex inline'>y =(-x)^4</code> and <code class='latex inline'>y = x^4</code></p><p>iii. <code class='latex inline'>y =(-x)^6</code> and <code class='latex inline'>y = x^6</code></p>
<p>Without graphing, determine if each polynomial function has line symmetry, point symmetry or neither. </p><p><code class='latex inline'> \displaystyle p(x) = -5x^3 + 2x </code></p>
<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>Roy noticed that the graph of the function <code class='latex inline'>f(x) =ax^b -cx</code> is symmetrical with respect to the origin, and that it has some turning points. Does the graph have an odd, even or no number of turning points?</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/169" />
<p> Determine whether each graph represents an even-degree or an odd-degree polynomial function. Explain your reasoning.</p><img src="/qimages/297" />
<p>State whether each function is even, odd, or neither. Show your work.</p><p><code class='latex inline'>f(x) = (x - 4)(x + 3)(2x - 1)</code></p>
<p>What is the value of <code class='latex inline'>f(-3) + f(3)</code> if <code class='latex inline'>f(x)</code> is an odd function and <code class='latex inline'>f(3) = 2</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>Determine if the function is even or odd or neither.</p><p><code class='latex inline'> \displaystyle P(x) = x^5 + 6x^3 - 2x </code></p>
<p>Graph each pair of functions. What do you notice? Provide an algebraic explanation for what you observe.</p><p>i. <code class='latex inline'>y =(-x)^3</code> and <code class='latex inline'>y = -x^3</code></p><p>ii. <code class='latex inline'>y =(-x)^5</code> and <code class='latex inline'>y = -x^5</code></p><p>iii. <code class='latex inline'>y =(-x)^7</code> and <code class='latex inline'>y = -x^7</code></p>
<p>Determine, algebraically, whether each function has point symmetry about the origin or line symmetry about the y-axis. State whether each function is even, odd, or neither. Show your work.</p><p> <code class='latex inline'>g(x) = -2(x + 2)(x -2)(1+x)(x -1)</code></p>
<p>For the graphs below</p> <ul> <li>(a) State the least possible degree.</li> <li>(b) State the sign of the leading coefficient.</li> <li>(c) Describe the end behaviour of the graph.</li> <li>(d) Identify the type of symmetry, if it exists.</li> </ul> <img src="/qimages/297" />
<p>A function is said to be even if <code class='latex inline'>f(-x) = f(x)</code> for all values of . A function is said to be odd if <code class='latex inline'>f(-x) = -f(x)</code> for all values of <code class='latex inline'>x</code>.</p> <ul> <li>Is the function <code class='latex inline'>y = \tan x</code> even, odd, or neither?</li> </ul>
<ul> <li>i. Determine whether each function even, odd, or neither. Explain.</li> <li>ii. Without graphing, determine if each polynomial function has line symmetry about the y-axis. point symmetry about the origin, or neither. Explain.</li> </ul> <p><code class='latex inline'>y= x(2x +1)^2(x-4)</code></p>
<p>Determine, algebraically, whether each function has point symmetry about the origin or line symmetry about the y-axis. State whether each function is even, odd, or neither. Show your work.</p><p><code class='latex inline'>h(x) = (3x + 2)^2(x -4)(1+x)(2x -3)</code></p>
<p>Without graphing, determine if each polynomial function has line symmetry, point symmetry or neither. </p><p><code class='latex inline'> \displaystyle f(x) = -6x^5 + 2x </code></p>
<ul> <li>i. Determine whether each function even, odd, or neither. Explain.</li> <li>ii. Without graphing, determine if each polynomial function has line symmetry about the y-axis. point symmetry about the origin, or neither. Explain.</li> </ul> <p><code class='latex inline'>y = -2x^6 + x^4 + 8</code></p>
<p>A function is said to be even if <code class='latex inline'>f(-x) = f(x)</code> for all values of . A function is said to be odd if <code class='latex inline'>f(-x) = -f(x)</code> for all values of <code class='latex inline'>x</code>.</p><p>Is the function <code class='latex inline'>y = \sin x</code> even, odd, or neither?</p>
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