Chapter 5

Expand: \(\log _{b}(x \sqrt[3]{y})\) (Section \(4.3, \text { Example } 4)\)

Solve: \(\frac{x}{x-3}=\frac{3}{x-3}-\frac{3}{4}\)

Will help you prepare for the material covered in the next section. a. Graph \(y=-3 \cos \frac{x}{2}\) for \(-\pi \leq x \leq 5 \pi\) b. Consider the reciprocal function of \(y=-3 \cos \frac{x}{2}\) namely, \(y=-3 \sec \frac{k}{2} .\) What does your graph from part (a) indicate about this reciprocal function for \(x=-\pi, \pi, 3 \pi,\) and \(5 \pi ?\)

Write as a single logarithm: \(\frac{1}{2} \log x+6 \log (x-2)\) (Section \(4.3, \text { Example } 6)\)

Solve: \(\quad x^{2}+4 x+6=0\)

Graph: \(f(x)=\frac{5 x+1}{x-1}\) (Section \(3.5, \text { Example } 5)\)

Let \(f(x)=\left\\{\begin{array}{ll}{x^{2}+2 x-1} & {\text { if } x \geq 2} \\\ {3 x+1} & {\text { if } x<2}\end{array}\right.\) Find \(f(5)-f(-5)\)

Exercises \(127-129\) will help you prepare for the material covered in the next section. In each exercise, let \(\theta\) be an acute angle in a right triangle, as shown in the figure. These exercises require the use of the Pythagorean Theorem. If \(a=1\) and \(b=1,\) find the ratio of the length of the side opposite \(\theta\) to the length of the hypotenuse. Simplify the ratio by rationalizing the denominator.

Exercises \(127-129\) will help you prepare for the material covered in the next section. Determine the amplitude and period of \(y=10 \cos \frac{\pi}{6} x\).