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Chapter 1: Problem 83

When plotting points on the rectangular coordinate system, is it true that the scales on the \(x\) - and \(y\) -axes must be the same? Explain.

Short Answer

Expert verified
No, the scales on the \(x\) - and \(y\) -axes do not necessarily have to be the same when plotting points on the rectangular coordinate system. The scales may differ based on the data to be plotted for better readability and interpretation.

Step by step solution

01

Understand the coordinate system

A rectangular coordinate system is a two-dimensional graph, which has two perpendicular lines, or axes, labeled \(x\) and \(y\). This system is used to define positions (x, y) or coordinates on the plane.
02

Understand the concept of scale in the coordinate system

The scale refers to the numbers marked on the axes, it determines the relationship between the units on the graph and the actual values they represent.
03

Answer the problem

The scales on the \(x\) - and \(y\) -axes do not have to be the same. Depending on the nature and range of the data to be displayed, different scales may be used for the two axes to make the plotted data more readable and interpretable. It is, however, important to ensure that the scales are properly labelled to avoid misinterpretation.

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Most popular questions from this chapter

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. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^{2} & & & & & \\ \hline \end{array}$$ $$ k=1 $$

Determine whether the function has an inverse function. If it does, find the inverse function. $$ g(x)=\frac{x}{8} $$

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. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^{2} & & & & & \\ \hline \end{array}$$ $$ k=\frac{1}{2} $$

Use the functions given by \(f(x)=x+4\) and \(g(x)=2 x-5\) to find the specified function. $$ g^{-1} \circ f^{-1} $$

Find a mathematical model for the verbal statement. \(F\) varies directly as \(g\) and inverselv as \(r^{2}\).
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