91Ó°ÊÓ

Graph the functions. $$y=\frac{1}{x+2}$$

Tell by what factor and direction the graphs of the given functions are to be stretched or compressed. Give an equation for the stretched or compressed graph. \(y=1-x^{3}, \quad\) compressed horizontally by a factor of 3

Match each equation with its graph. Do not use a graphing device, and give reasons for your answer. (GRAPHS CANNOT COPY) a. \(y=5 x\) b. \(y=5^{x}\) c. \(y=x^{5}\)

Express the ratios as ratios of natural logarithms and simplify. a. \(\frac{\log _{9} x}{\log _{3} x}\) b. \(\frac{\log _{\sqrt{10}} x}{\log _{\sqrt{2}} x}\) c. \(\frac{\log _{a} b}{\log _{b} a}\)

For a curve to be symmetric about the \(x\) -axis, the point \((x, y)\) must lie on the curve if and only if the point \((x,-y)\) lies on the curve. Explain why a curve that is symmetric about the \(x\) -axis is not the graph of a function, unless the function is \(y=0.\)

Suppose that the range of \(g\) lies in the domain of \(f\) so that the composite \(f \circ g\) is defined. If \(f\) and \(g\) are one-to-one, can anything be said about \(f \circ g ?\) Give reasons for your answer.

Graph the function \(y=\sqrt{|x|}\).

Radioactive decay The half-life of a certain radioactive substance is 12 hours. There are 8 grams present initially. a. Express the amount of substance remaining as a function of time \(t\) b. When will there be 1 gram remaining?

Population growth The population of Glenbrook is 375,000 and is increasing at the rate of \(2.25 \%\) per year. Predict when the population will be 1 million.