91Ó°ÊÓ

Find the indicated values of the function by hand and by using the table feature of a calculator (or the EVAL key on TI-85/86). If your answers do not agree with each other or with those at the back of the book, you are either making algebraic mistakes or incorrectly entering the function in the equation memory. \(f(x)=\frac{x-3}{x^{2}+4}\) (d) \(f(2)\) (a) \(f(-1)\) (b) \(f(0)\) (c) \(f(1)\) (e) \(f(3)\)

Deal with the greatest integer function of Example \(7,\) which is given by the equation \(y=[x]\). Compute the following values of the function: $$[6.75]$$

Deal with the greatest integer function of Example \(7,\) which is given by the equation \(y=[x]\). Compute the following values of the function: $$[1.75]$$

Use a calculator and the Horizontal Line Test to determine whether or not the function \(f\) is one-to-one. $$f(x)=.1 x^{3}-.1 x^{2}-.005 x+1$$

Describe a sequence of transformations that will transform the graph of the function \(f\) into the graph of the function \(g.\) $$f(x)=x^{2}+x ; \quad g(x)=(x-3)^{2}+(x-3)+2$$

(a) Use the fact that the absolute value function is piecewise-defined (see Example 7) to write the rule of the given function as a piecewise-defined function whose rule does not include any absolute value bars. (b) Graph the function. $$g(x)=|x|-4$$

Use the Round-Trip Theorem on page 223 to show that \(g\) is the inverse of \(f\) $$f(x)=2 x-6, \quad g(x)=\frac{x}{2}+3$$

Write the rule of a function g whose graph can be obtained from the graph of the function \(f\) by performing the transformations in the order given. \(f(x)=x^{2}+2 ;\) shift the graph horizontally 5 units to the left and then vertically upward 4 units.

Use the Round-Trip Theorem on page 223 to show that \(g\) is the inverse of \(f\) $$f(x)=\frac{-3}{2 x+5}, \quad g(x)=\frac{-3-5 x}{2 x}$$

Use the Round-Trip Theorem on page 223 to show that \(g\) is the inverse of \(f\) $$f(x)=x^{3}-1, \quad g(x)=\sqrt[3]{x+1}$$