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Chapter 1: Problem 6
Fill in the blanks. When you construct and use a table to solve a problem, you are using a _____ approach.
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Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\left\\{\begin{array}{ll} x+3, & x<0 \\ 6-x, & x \geq 0 \end{array}\right. $$
The mathematical model \(y=\frac{\kappa}{x}\) is an example of _____ variation.
Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\sqrt{2 x+3} $$
Determine whether the variation model is of the form \(y=k x\) or \(y=k / x,\) and find \(k .\) Then write \(a\) model that relates \(y\) and \(x\). $$ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 10 & 15 & 20 & 25 \\ \hline y & -3.5 & -7 & -10.5 & -14 & -17.5 \\ \hline \end{array} $$
Use the given value of \(k\) to complete the table for the inverse variation model $$y=\frac{k}{x^{2}}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=\frac{k}{x^{2}} & & & & & \\ \hline \end{array}$$ $$ k=5 $$
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