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Chapter 1: Problem 8
Find the domain of each function. $$g(x)=\frac{2}{x^{2}+x-12}$$
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Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$g(x)=x^{\frac{2}{3}}$$
Here is the Federal Tax Rate Schedule \(X\) that specifies the tax owed by a
single taxpayer for a recent year. (TABLE CANNOT COPY)
The preceding tax table can be modeled by a piecewise function, where \(x\)
represents the taxable income of a single taxpayer and \(T(x)\) is the tax owed:
$$T(x)=\left\\{\begin{array}{ccc}
0.10 x & \text { if } & 0
Show that the points \(A(1,1+d), B(3,3+d),\) and \(C(6,6+d)\) are collinear (lie along a straight line) by showing that the distance from \(A\) to \(B\) plus the distance from \(B\) to \(C\) equals the distance from \(A\) to \(C\).
Use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. $$(y+1)^{2}=36-(x-3)^{2}$$
Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{3}-6 x^{2}+9 x+1$$
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