Chapter 3: Problem 3
A set of points in the \(x y\) -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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Determine algebraically whether each function is even, odd, or neither. \(F(x)=\frac{2 x}{|x|}\)
Determine which of the given points are on the graph of the equation \(y=3 x^{2}-8 \sqrt{x}\). Points: (-1,-5),(4,32),(9,171)
The slope of the secant line containing the two points \((x, f(x))\) and \((x+h, f(x+h))\) on the graph of a function \(y=f(x)\) may be given as \(m_{\mathrm{sec}}=\frac{f(x+h)-f(x)}{(x+h)-x}=\frac{f(x+h)-f(x)}{h} \quad h \neq 0\) (a) Express the slope of the secant line of each function in terms of \(x\) and \(h\). Be sure to simplify your answer. (b) Find \(m_{\text {sec }}\) for \(h=0.5,0.1\), and 0.01 at \(x=1 .\) What value does \(m_{\text {sec }}\) approach as h approaches \(0 ?\) (c) Find an equation for the secant line at \(x=1\) with \(h=0.01\). (d) Use a graphing utility to graph fand the secant line found in part ( \(c\) ) in the same viewing window. Problems \(85-92\) require the following discussion of a secant line. The slope of the secant line containing the two points \((x, f(x))\) and \((x+h, f(x+h))\) on the graph of a function \(y=f(x)\) may be given as \(m_{\mathrm{sec}}=\frac{f(x+h)-f(x)}{(x+h)-x}=\frac{f(x+h)-f(x)}{h} \quad h \neq 0\) (a) Express the slope of the secant line of each function in terms of \(x\) and \(h\). Be sure to simplify your answer. (b) Find \(m_{\text {sec }}\) for \(h=0.5,0.1\), and 0.01 at \(x=1 .\) What value does \(m_{\text {sec }}\) approach as h approaches \(0 ?\) (c) Find an equation for the secant line at \(x=1\) with \(h=0.01\). (d) Use a graphing utility to graph fand the secant line found in part ( \(c\) ) in the same viewing window. \(f(x)=2 x^{2}-3 x+1\)
Rotational Inertia The rotational inertia of an object varies directly with the square of the perpendicular distance from the object to the axis of rotation. If the rotational inertia is \(0.4 \mathrm{~kg} \cdot \mathrm{m}^{2}\) when the perpendicular distance is \(0.6 \mathrm{~m},\) what is the rotational inertia of the object if the perpendicular distance is \(1.5 \mathrm{~m} ?\)
The total worldwide digital music revenues \(R\), in billions of dollars, for the years 2012 through 2017 can be modeled by the function $$ R(x)=0.15 x^{2}-0.03 x+5.46 $$ where \(x\) is the number of years after 2012 . (a) Find \(R(0), R(3),\) and \(R(5)\) and explain what each value represents. (b) Find \(r(x)=R(x-2)\) (c) Find \(r(2), r(5)\) and \(r(7)\) and explain what each value represents. (d) In the model \(r=r(x),\) what does \(x\) represent? (e) Would there be an advantage in using the model \(r\) when estimating the projected revenues for a given year instead of the model \(R ?\)
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