27.1: Review of functions and graphs
- Page ID
- 68482
Find all solutions of the equation: \(\big| 3x-9\big| =6\)
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\(x = 1\) or \(x = 5\)
Find the equation of the line displayed below.
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\(y=-\dfrac{1}{2} x+1\)
Find the solution of the equation: \(x^3-3x^2+2x-2=0\) Approximate your answer to the nearest hundredth.
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\(x \approx 2.52\)
Let \(f(x)=x^2-2x+5\). Simplify the difference quotient \(\dfrac{f(x+h)-f(x)}{h}\) as much as possible.
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\(2 x-2+2 h\)
Consider the following graph of a function \(f\).
Find: domain of \(f\), range of \(f\), \(f(3)\), \(f(5)\), \(f(7)\), \(f(9)\).
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domain \(D=[2,7]\), range \(R=(1,4], f(3)=2, f(5)=2, f(7)=4, f(9) \) is undefined
Find the formula of the graph displayed below.
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\(f(x)=-x^{2}+2\)
Let \(f(x)=5x+4\) and \(g(x)=x^2+8x+7\). Find the quotient \(\left(\dfrac f g\right)(x)\) and state its domain.
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\(\left(\dfrac{f}{g}\right)(x)=\dfrac{5 x+4}{x^{2}+8 x+7}=\dfrac{5 x+4}{(x+7)(x+1)}\) has domain \(D=\mathbb{R}-\{-7,-1\}\)
Let \(f(x)=x^2+\sqrt{x-3}\) and \(g(x)=2x-3\). Find the composition \((f\circ g)(x)\) and state its domain.
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\((f \circ g)(x)=4 x^{2}-12 x+9+\sqrt{2 x-6}\) has domain \(D=[3, \infty)\)
Consider the assignments for \(f\) and \(g\) given by the table below.
\[\begin{array}{|c||c|c|c|c|c|}
\hline x & 2 & 3 & 4 & 5 & 6 \\
\hline f(x) & 5 & 0 & 2 & 4 & 2 \\
\hline g(x) & 6 & 2 & 3 & 4 & 1 \\
\hline
\end{array} \nonumber \]
Is \(f\) a function? Is \(g\) a function? Write the composed assignment for \((f\circ g)(x)\) as a table.
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\(f\) and \(g\) are both functions, and the composition is given by the table:
\(\begin{array}{|c||c|c|c|c|c|}
\hline x & 2 & 3 & 4 & 5 & 6 \\
\hline \hline f(x) & 5 & 0 & 2 & 4 & 2 \\
\hline g(x) & 6 & 2 & 3 & 4 & 1 \\
\hline(f \circ g)(x) & 2 & 5 & 0 & 2 & \text { undef. } \\
\hline
\end{array}\)
Find the inverse of the function \(f(x)=\dfrac{1}{2x+5}\).
- Answer
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\(f^{-1}(x)=\dfrac{1}{2 x}-\dfrac{5}{2}\)