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Chapter 1: Problem 10
Fill in the blank: The constant function and the identity function are two special types of _____ functions.
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(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{x-3}{x+2} $$
An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). (a) The table shows the volumes \(V\) (in cubic centimeters) of the box for various heights \(x\) (in centimeters). Use the table to estimate the maximum volume. $$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Height, } x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Volume, } V & 484 & 800 & 972 & 1024 & 980 & 864 \\ \hline \end{array}$$ (b) Plot the points \((x, V)\) from the table in part (a). Does the relation defined by the ordered pairs represent \(V\) as a function of \(x\) ? (c) If \(V\) is a function of \(x\), write the function and determine its domain.
Two lines are _____ if and only if their slopes are equal.
Plot the points and find the slope of the line passing through the pair of points. $$ (12,0),(0,-8) $$
Match each function with its name. (a) squaring function (b) square root function (c) cubic function (d) linear function (e) constant function (f) absolute value function (g) greatest integer function (h) reciprocal function (i) identity function $$ f(x)=\sqrt{x} $$
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