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Chapter 2: Problem 42
What is the slope of a line that is perpendicular to the line whose equation is \(A x+B y+C=0, A \neq 0\) and \(B \neq 0 ?\)
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graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$ \begin{aligned} (x-2)^{2}+(y+3)^{2} &=4 \\ y &=x-3 \end{aligned} $$
Sketch the graph of \(f\) using the following properties. (More than one correct graph is possible.) \(f\) is a piecewise function that is decreasing on \((-\infty, 2), f(2)=0, f\) is increasing on \((2, \infty),\) and the range of \(f\) is \([0, \infty)\)
If \(f(x+y)=f(x)+f(y)\) and \(f(1)=3,\) find \(f(2), f(3)\) and \(f(4) .\) Is \(f(x+y)=f(x)+f(y)\) for all functions?
(For assistance with this exercise, refer to the discussion of piecewise functions beginning on page 234 , as well as to Exercises \(79-80 .\) ) Group members who have cellphone plans should describe the total monthly cost of the plan as follows: \(\$ ________\) per month buys ____________ minutes. Additional time costs $\$$ __________per minute.
determine whether each statement makes sense or does not make sense, and explain your reasoning. The graph of \((x-3)^{2}+(y+5)^{2}=-36\) is a circle with radius 6 centered at \((3,-5)\)
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