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Chapter 1: Problem 5

Plot the points in the Cartesian plane. $$(-4,2),(-3,-6),(0,5),(1,-4),(0,0),(3,1)$$

Short Answer

Expert verified
The points (-4,2),(-3,-6),(0,5),(1,-4),(0,0),(3,1) have been successfully plotted on the Cartesian plane. Make sure each point aligns with its coordinates on the x and y axis.

Step by step solution

01

Understand the Coordinate System

In a Cartesian plane, each point is defined by a pair of numbers (x, y). The first number, x, refers to the position on the horizontal axis, and the second number, y, refers to the position on the vertical axis.
02

Plot the first point (-4,2)

Start at the origin (0,0), move 4 units to the left (since x is -4) and then move 2 units upwards (since y is 2) to reach the point (-4,2). Mark this point on the plane.
03

Plot the second point (-3,-6)

Start at the origin, move 3 units to the left and 6 units downwards to reach the point (-3,-6). Mark this point on the plane.
04

Plot the third point (0,5)

Start at the origin, stay at the origin for the x value (since x is 0) and move 5 units upwards to reach the point (0,5). Mark this point on the plane.
05

Plot the fourth point (1,-4)

Start at the origin, move 1 unit to the right and then 4 units downwards to reach the point (1,-4). Mark this point on the plane.
06

Plot the fifth point (0,0)

This point is the origin itself, so we do not need to move anywhere.
07

Plot the sixth point (3,1)

Start at the origin, move 3 units to the right and then 1 unit upwards to reach the point (3,1). Mark this point on the plane.

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Most popular questions from this chapter

The cost per unit in the production of an MP3 player is 60 dollars. The manufacturer charges 90 dollars per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by 0.15 dollars per MP3 player for each unit ordered in excess of 100 (for example, there would be a charge of 87 dollars per MP3 player for an order size of 120 ). (a) The table shows the profits \(P\) (in dollars) for various numbers of units ordered, \(x .\) Use the table to estimate the maximum profit. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Units, } x & 130 & 140 & 150 & 160 & 170 \\\\\hline \text { Profit, } P & 3315 & 3360 & 3375 & 3360 & 3315 \\\\\hline\end{array}$$ (b) Plot the points \((x, P)\) from the table in part (a). Does the relation defined by the ordered pairs represent \(P\) as a function of \(x ?\) (c) Given that \(P\) is a function of \(x,\) write the function and determine its domain. (Note: \(P=R-C\) where \(R\) is revenue and \(C\) is cost.)

Consider \(f(x)=\sqrt{x-2}\) and \(g(x)=\sqrt[3]{x-2}\) Why are the domains of \(f\) and \(g\) different?

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Determine whether the statement is true or false. Justify your answer. Every relation is a function.
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