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Chapter 1: Problem 12
Plot the given point in a rectangular coordinate system. $$\left(-\frac{5}{2}, \frac{3}{2}\right)$$
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Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?
Given an equation in \(x\) and \(y,\) how do you determine if its graph is symmetric with respect to the \(x\) -axis?
114\. If \(f(x)=x^{2}-4\) and \(g(x)=\sqrt{x^{2}-4},\) then \((f \circ g)(x)=-x^{2}\) and \(\left(f^{\circ} g\right)(5)=-25\) 115\. There can never be two functions \(f\) and \(g\), where \(f \neq g\), for which \((f \circ g)(x)=(g \circ f)(x)\) 116\. If \(f(7)=5\) and \(g(4)=7,\) then \((f \circ g)(4)=35\) 117\. If \(f(x)=\sqrt{x}\) and \(g(x)=2 x-1,\) then \((f \circ g)(5)=g(2)\) 118\. Prove that if \(f\) and \(g\) are even functions, then \(f g\) is also an even function. 119\. Define two functions \(f\) and \(g\) so that \(f^{\circ} g=g \circ f\)
Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned}(x-2)^{2}+(y+3)^{2} &=4 \\\y &=x-3\end{aligned}$$
Given an equation in \(x\) and \(y,\) how do you determine if its graph is symmetric with respect to the \(y\) -axis?
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