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If \(f\) is a function defined by \(y=f ( x ) \), then \(x\) is called the _____ variable and \(y\) is the _____ variable.

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True or False  The independent variable is sometimes referred to as the argument of the function.

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True or False  If no domain is specified for a function \(f,\) then the domain of \(f\) is taken to be the set of all real numbers.

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True or False  The domain of the function \(f ( x ) =\dfrac{3 ( x^{2}-1 ) }{x-1}\) is \( \{ x|x\neq \pm 1 \} .\)

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True or False  A function can have more than one \(y\)-intercept.

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A set of points in the \(xy\)-plane is the graph of a function if and only if every _____ line intersects the graph in at most one point.

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If the point \(( 5,-3 ) \) is on the graph of \(f\), then \(f(\) _____ \()\) \(=\) _____.

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Find \(a\) so that the point \(( -1,2 ) \) is on the graph of \(f( x ) =ax^{2}+4\).

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Multiple Choice A function \(f\) is [(a) increasing, (b) decreasing, (c) nonincreasing, (d) nondecreasing, (e) constant] on an interval \(I\) if, for any choice of \(x_{1}\) and \(x_{2}\) in \(I,\) with \(x_{1}<x_{2}\), then \(f( x_{1}) <f( x_{2}) \).

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Multiple Choice A function \(f\) is [(a) even, (b) odd, (c) neither even nor odd] if for every number \(x\) in its domain, the number \(-x\) is also in the domain and \(f( -x) =f( x) \). A function \(f\) is [(a) even, (b) odd, (c) neither even nor odd] if for every number \(x\) in its domain, the number \(-x\) is also in the domain and \(f( -x) =-f( x) \).

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True or False  Even functions have graphs that are symmetric with respect to the origin.

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The average rate of change of \(f( x) =2x^{3}-3\) from \(0\) to \(2\) is _____.

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\(f( x) =3x^{2}+2x-4\)

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\(f( x) =\dfrac{x}{x^{2}+1}\)

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\(f(x) =\vert x\vert +4 \)

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\(f( x) = \sqrt{3-x}\)

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\(f( x) =x^{3}-1\)

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\(f( x) =\dfrac{x}{x^{2}+1}\)

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\(v( t) = \sqrt{t^{2}-9}\)

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\(g( x) = \sqrt{\dfrac{2}{x-1}}\)

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\(h( x) =\dfrac{x+2}{x^{3}-4x}\)

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\(s( t) =\dfrac{ \sqrt{t+1}}{t-5}\)

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\(f ( x) =-3x+1\)

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\(f ( x) =\dfrac{1}{x+3}\)

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\(f ( x) = \sqrt{x+7}\)

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\(f ( x) =\dfrac{2}{ \sqrt{x+7}}\)

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\(f ( x) =x^{2}+2x\)

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\(f ( x) = ( 2x+3) ^{2}\)

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\(f( x) =\left\{ \begin{array}{l@{\qquad}l@{\quad}l} x+3 & {\rm if}& -2\leq x<1 \\ 5 & {\rm if}& x=1 \\ -x+2 & {\rm if}& x>1 \end{array} \right. \)

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\(f( x) =\left\{ \begin{array}{l@{\qquad}l@{\quad}l} 2x+5 & {\rm if} & -3\leq x<0 \\ -3 & {\rm if} & x=0 \\ -5x & {\rm if} & x>0 \end{array} \right. \)

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\(f( x) =\left\{ \begin{array}{l@{\qquad}l@{\quad}l} 1+x & {\rm if} & x<0 \\ x^{2} & {\rm if} & x\geq 0 \end{array} \right.\)

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\(f( x) =\left\{ \begin{array}{l@{\qquad}l@{\quad}l} \dfrac{1}{x} & {\rm if} & x<0 \\ \sqrt[3]{x} & {\rm if} & x\geq 0 \end{array} \right.\)

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Find \(f ( 0) \) and \(f( -6)\).

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Is \(f ( 3) \) positive or negative?

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Is \(f ( -4) \) positive or negative?

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For what values of \(x\) is \(f ( x) =0\)?

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For what values of \(x\) is \(f ( x) >0\)?

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What is the domain of \(f\)?

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What is the range of \(f\)?

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What are the \(x\)-intercepts?

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What is the \(y\)-intercept?

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How often does the line \(y=\dfrac{1}{2}\) intersect the graph?

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How often does the line \(x=5\) intersect the graph?

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For what values of \(x\) does \(f( x) =3\)?

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For what values of \(x\) does \(f( x) =-2\)?

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On what interval(s) is the function \(f\) increasing?

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On what interval(s) is the function \(f\) decreasing?

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On what interval(s) is the function \(f\) constant?

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On what interval(s) is the function \(f\) nonincreasing?

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On what interval(s) is the function \(f\) nondecreasing?

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What is the domain of \(g\)?

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Is the point \(( 3,14) \) on the graph of \(g\)?

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If \(x=4\), what is \(g( x) \)? What is the corresponding point on the graph of \(g\)?

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If \(g( x) =2\), what is \(x\)? What is(are) the corresponding point(s) on the graph of \(g\)?

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List the \(x\)-intercepts, if any, of the graph of \(g\).

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What is the \(y\)-intercept, if there is one, of the graph of \(g\)?

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\(h( x) =\dfrac{x}{x^{2}-1}\)

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\(f( x) =\sqrt[3]{3x^{2}+1} \)

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\(G( x) = \sqrt{x}\)

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\(F( x) =\dfrac{2x}{\vert x\vert }\)

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Find the average rate of change of \(f(x) =-2x^{2}+4\):

1. From \(1\) to \(2\)
2. From \(1\) to \(3\)
3. From \(1\) to \(4\)
4. From \(1\) to \(x\), \(x\neq 1\)

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Find the average rate of change of \(s( t) =20-0.8t^{2}\):

1. From \(1\) to \(4\)
2. From \(1\) to \(3\)
3. From \(1\) to \(2\)
4. From \(1\) to \(t\), \(t\neq 1\)

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The monthly cost \(C\), in dollars, of manufacturing \(x\) road bikes is given by the function \[ C( x) =0.004x^{3}-0.6x^{2}+250x+100{,}500 \]

1. Find the average rate of change of the cost \(C\) of manufacturing from \( 100\) to \(101\) road bikes.
2. Find the average rate of change of the cost \(C\) of manufacturing from \( 500\) to \(501\) road bikes.
3. Interpret the results from parts (a) and (b).

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The weekly cost in dollars to produce \(x\) tons of steel is given by the function \[ C( x) =\dfrac{1}{10}x^{2}+5x+1500 \]

1. Find the average rate of change of the cost \(C\) of producing from \(500\) to \(501\) tons of steel.
2. Find the average rate of change of the cost \(C\) of producing from \(1000\) to \(1001\) tons of steel.
3. Interpret the results from parts (a) and (b).