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Chapter 1: Problem 9
Find the domain of each function. $$f(x)=\frac{1}{x+7}+\frac{3}{x-9}$$
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A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at this point of contact. Write an equation in point-slope form for the line tangent to the circle whose equation is \(x^{2}+y^{2}=25\) at the point (3,-4).
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 \(C\).
Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned}x^{2}+y^{2} &=9 \\\x-y &=3\end{aligned}$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. My graph is decreasing on \((-\infty, a)\) and increasing on \((a, \infty)\) so \(f(a)\) must be a relative maximum.
What does it mean if a function \(f\) is increasing on an interval?
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