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Chapter 1: Problem 14
Find the coordinates of the point. The point is on the \(x\) -axis and 12 units to the left of the \(y\) -axis.
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Use the given value of \(k\) to complete the table for the direct variation model $$y=k x^{2}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^{2} & & & & & \\ \hline \end{array}$$ $$ k=\frac{1}{4} $$
Assume that \(y\) is directly proportional to \(x\). Use the given \(x\) -value and \(y\) -value to find a linear model that relates \(y\) and \(x\). $$ x=5, y=12 $$
Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\left\\{\begin{array}{ll} x+3, & x<0 \\ 6-x, & x \geq 0 \end{array}\right. $$
When buying gasoline, you notice that 14 gallons of gasoline is approximately the same amount of gasoline as 53 liters. Use this information to find a linear model that relates liters \(y\) to gallons \(x\). Then use the model to find the numbers of liters in 5 gallons and 25 gallons.
Use the functions given by \(f(x)=x+4\) and \(g(x)=2 x-5\) to find the specified function. $$ g^{-1} \circ f^{-1} $$
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