Chapter 1: Problem 17
In Exercises \(17-20,\) write the slope-intercept equation for the line with slope \(m\) and \(y\) -intercept \(b\) . $$m=3, \quad b=-2$$
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Multiple Choice Which of the following gives the range of \(f(x)=1+\frac{1}{x-1} ?\) \(\begin{array}{ll}{(\mathbf{A})(-\infty, 1) \cup(1, \infty)} & {(\mathbf{B}) x \neq 1} \\ {(\mathbf{D})(-\infty, 0) \cup(0, \infty)} & {(\mathbf{E}) x \neq 0}\end{array}\)
In Exercises \(39-42,\) draw the graph and determine the domain and range of the function. $$y=\log _{3}(x-4)$$
In Exercises \(39-42,\) draw the graph and determine the domain and range of the function. $$y=-3 \log (x+2)+1$$
Explorations Hyperbolas Let \(x=a \sec t\) and \(y=b \tan t\) (a) Writing to Learn Let \(a=1,2,\) or \(3, b=1,2,\) or \(3,\) and graph using the parameter interval \((-\pi / 2, \pi / 2)\) . Explain what you see, and describe the role of \(a\) and \(b\) in these parametric equations. (Caution: If you get what appear to be asymptomes, try using the approximation \([-1.57,1.57]\) for the parameter interval.) (b) Let \(a=2, b=3,\) and graph in the parameter interval \((\pi / 2,3 \pi / 2)\) . Explain what you see. (c) Writing to Learn Let \(a=2, b=3,\) and graph using the parameter interval \((-\pi / 2,3 \pi / 2) .\) Explain why you must be careful about graphing in this interval or any interval that contains \(\pm \pi / 2\) . (d) Use algebra to explain why \(\left(\frac{x}{a}\right)^{2}-\left(\frac{y}{b}\right)^{2}=1\) (e) Let \(x=a\) tan \(t\) and \(y=b\) sec \(t .\) Repeat (a), (b), and (d) using an appropriate version of \((\mathrm{d}) .\)
In Exercises \(27-30\) , give the measure of the angle in radians and degrees. Give exact answers whenever possible. $$\tan ^{-1}(-5)$$
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