10. Q10c
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Similar Question 1
<p>Evaluate, where <code class='latex inline'>f(x)=2-3x</code>.</p><p><code class='latex inline'> \displaystyle \begin{array}{ccccc} & (a) & f(2) &(c)& f(-4) &(e)& f(a) \\ & (b) & f(0) &(d) &f(\frac{1}{2}) &(f) & f(3b) \end{array} </code></p>
Similar Question 2
<p>As a mental arithmetic exercise, a teacher asked her students to think of a number, triple it, and subtract the resulting number from 24. Finally, they were asked to multiply the resulting difference by the number they first thought of.</p><p><strong>(a)</strong> Use function notation to express the final answer in terms of the original number.</p><p><strong>(b)</strong> Determine the result of choosing numbers 3, -5, 10.</p><p><strong>(c)</strong> Determine the maximum result possible.</p>
Similar Question 3
<p>Let <code class='latex inline'>f(x)=x^2+2x-15</code>. Determine the values of <code class='latex inline'>x</code> for which</p><p><code class='latex inline'> \displaystyle f(x)=-16 </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>Consider the function <code class='latex inline'>g(t)=3t+5</code>.</p><p>Determine each value. </p><p><code class='latex inline'> \displaystyle \begin{array}{ccccccc} &(i)& g(0) &(iv)& g(2)-g(1) \\ &(ii)& g(3) &(v)& g(1001)-g(1000) \\ &(iii)& g(1)-g(0) &(vi)& g(a+1)-g(a) \\ \end{array} </code></p>
<p>Graph the function <code class='latex inline'>f(x)=3(x-1)^2-4</code>.</p>
<p>Given that value of <code class='latex inline'>f(1) = 3</code> and <code class='latex inline'>f(4) = -3</code>, find the value of <code class='latex inline'>f(-1) + f(-4)</code> if <code class='latex inline'>f(x)</code> is an even function.</p>
<p>Given the function <code class='latex inline'>h(x) = 2x + 7</code>, what is <code class='latex inline'>\displaystyle \frac{h(9) - h(3)}{9 -3}</code>?</p>
<p>Evaluate <code class='latex inline'>f(-1)</code>,<code class='latex inline'>f(3)</code>, and <code class='latex inline'>f(1.5)</code> for </p><p><code class='latex inline'> \displaystyle f(x)=(x-2)^2-1 </code></p>
<p>For <code class='latex inline'>h(x)=2x-5</code>, determine</p><p><code class='latex inline'> \displaystyle \begin{array}{ccccc} &(a)& h(a) &(c)& h(3c-1) \\ & (b)& h(b+1) &(d) &h(2-5x) \\ \end{array} </code></p>
<p>Let <code class='latex inline'>f(x)=x^2+2x-15</code>. Determine the values of <code class='latex inline'>x</code> for which</p><p><code class='latex inline'> \displaystyle f(x)=-12 </code></p>
<p>Evaluate <code class='latex inline'>f(-1)</code>,<code class='latex inline'>f(3)</code>, and <code class='latex inline'>f(1.5)</code> for </p><p><code class='latex inline'> \displaystyle f(x)=2+3x-4x^2 </code></p>
<p>The graph at the right shows <code class='latex inline'>f(x)=2(x-3)^2-1</code>.</p><img src="/qimages/4703" /><p>What does <code class='latex inline'>f(-2)</code> represent on the graph of <code class='latex inline'>f</code>?</p><p>Evaluate <code class='latex inline'>f(-2)</code></p>
<p>Evaluate, where <code class='latex inline'>f(x)=2-3x</code>.</p><p><code class='latex inline'> \displaystyle \begin{array}{ccccc} & (a) & f(2) &(c)& f(-4) &(e)& f(a) \\ & (b) & f(0) &(d) &f(\frac{1}{2}) &(f) & f(3b) \end{array} </code></p>
<p>Consider the function <code class='latex inline'>f(s)=s^2-6s+9</code>.</p><p><code class='latex inline'> \displaystyle \begin{array}{cccccc} &(i)& f(0) &(iv)& f(3) \\ &(ii) &f(1) &(v)& [f(2)-f(1)] - [f(1)-f(0)] \\ &(iii) &f(2) &(vi) & [f(3)-f(2)] - [f(2) - f(1)] \\ \end{array} </code></p><p><strong>(c)</strong> In part (b), what do you notice about the answers to parts (v) and (vi)? Explain why this happens.</p>
<p>For <code class='latex inline'>f(x)=\dfrac{1}{2x}</code>, determine</p><p><code class='latex inline'> \displaystyle \begin{array}{lllllllll} & (a)& f(-3) &(b) & f(0) \\ & (c) & f(1)-f(3) &(d) & f(\frac{1}{4})+f(\frac{3}{4}) \\ \end{array} </code></p>
<p>For <code class='latex inline'>f(x)=3(x-1)^2-4</code>, use the equation to determine</p><p><code class='latex inline'> \displaystyle \begin{array}{llllll} &(i)& f(2)-f(1) &(ii)& 2f(3)-7 &(iii)&f(1-x) \\ \end{array} </code></p>
<p>Let <code class='latex inline'>f(x)=x^2+2x-15</code>. Determine the values of <code class='latex inline'>x</code> for which</p><p><code class='latex inline'> \displaystyle f(x)=0 </code></p>
<p>The graphs of <code class='latex inline'>y=f(x)</code> and <code class='latex inline'>y=g(x)</code> are shown.</p><img src="/qimages/340" /><p>Use the graphs, evaluate</p><p><code class='latex inline'> \displaystyle \begin{array}{llllll} &(a) &f(1) &(c) & f(4)-g(-2) \\ & (b) & g(-2) &(d) & x \text{ when } f(x)=-3 \\ \end{array} </code></p>
<p>Let <code class='latex inline'>f(x)=3x+1</code> and <code class='latex inline'>g(x)=2-x</code>. Determine the values <code class='latex inline'>a</code> such that</p><p><code class='latex inline'> \displaystyle f(a)=g(a) </code></p>
<p>The highest and lowest marks awarded on an examination were 285 and 75. All marks must be reduced so that the highest and lowest marks become 200 and 60.</p><p><strong>(a)</strong> Determine a linear function that will convert 285 to 200 and 75 to 60.</p><p><strong>(b)</strong> Use the function to determine the new marks that correspond to original marks of 95,175,215, and 255. </p>
<p>For <code class='latex inline'>f(x)=3(x-1)^2-4</code>, what does <code class='latex inline'>f(-1)</code> equal to?</p>
<p>Write each function in mapping notation.</p><p>d) <code class='latex inline'>\displaystyle r(k)=\frac{1}{5 k-3} </code></p>
<p>The graph at the right shows <code class='latex inline'>f(x)=2(x-3)^2-1</code>.</p><img src="/qimages/4703" /><p>Evaluate <code class='latex inline'>f(-2)</code></p>
<p>For <code class='latex inline'>g(x)=4-5x</code>, determine the input for <code class='latex inline'>x</code> when the output of <code class='latex inline'>g(x)</code> is </p><p><code class='latex inline'> \displaystyle \begin{array}{ccccc} & (a) & -6 &(b) &2 & (c) & 0 &(d)& \frac{3}{5} \\ \end{array} </code></p>
<p>Let <code class='latex inline'>f(x)=x^2+2x-15</code>. Determine the values of <code class='latex inline'>x</code> for which</p><p><code class='latex inline'> \displaystyle f(x)=-16 </code></p>
<p>As a mental arithmetic exercise, a teacher asked her students to think of a number, triple it, and subtract the resulting number from 24. Finally, they were asked to multiply the resulting difference by the number they first thought of.</p><p><strong>(a)</strong> Use function notation to express the final answer in terms of the original number.</p><p><strong>(b)</strong> Determine the result of choosing numbers 3, -5, 10.</p><p><strong>(c)</strong> Determine the maximum result possible.</p>
<p>The second span of the Bluewater Bridge in Sarnia, Ontario, is supported by two parabolic arches. Each arch is set in concrete foundations that are on opposite sides of the St. Clair River. The feet of the arches are <code class='latex inline'>281 m</code> apart. The top of each arch rises <code class='latex inline'>71 m</code> above the river. Write a function to model the arch.</p>
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