91Ó°ÊÓ

find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$ f(x)=\frac{1}{x} $$

Begin by graphing the absolute value function, \(f(x)=|x|.\) Then use transformations of this graph to graph the given function. $$g(x)=-2|x+3|+2$$

Let \(f\) and \(g\) be defined by the following table: \(\begin{array}{rrr}{x} & {f(x)} & {g(x)} \\ {-2} & {6} & {0} \\ {-1} & {3} & {4} \\ {0} & {-1} & {1} \\ {1} & {-4} & {-3} \\ {2} & {0} & {-6}\end{array}\) Find \(\sqrt{f(-1)-f(0)}-[g(2)]^{2}+f(-2) \div g(2) \cdot g(-1)\)

Use a graphing utility to graph each equation in Exercises \(100-103\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. Check your result by using the coefficient of \(x\) in the line's equation. $$ y=2 x+4 $$

If equations for two functions are given, explain how to cobtain the quotient function and its domain.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used a function to model data from 1990 through 2015 . The independent variable in my model represented the number of years after 1990 , so the function's domain was \(\\{x | x=0,1,2,3, \ldots, 25\\}\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I must have made a mistake in finding the composite functions \(f \circ g\) and \(g \circ f,\) because I notice that \(f \circ g\) is not the same function as \(g \circ f\)

Furry Finances. A pet insurance policy has a monthly rate that is a function of the age of the insured dog or cat. For pets whose age does not exceed 4 , the monthly cost is \(\$ 20 .\) The cost then increases by \(\$ 2\) for each successive year of the pet's age.

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 \([0, \infty)\)