-Describe applications of the Cartesian coordinate system to plot a real-world s
ID: 2965262 • Letter: #
Question
-Describe applications of the Cartesian coordinate system to plot a real-world situation. In your description, indicate the characteristics of each coordinate, and a point in terms of specific x and y coordinates.
-Explain what the author means by "fickle picker" to help determine if a set of ordered pairs represents a function and how it can be used to identify a function. Provide an example.
-Explain whether it matters or does not matter which values you pick for x when you graph a line by plotting points. Explain your reasoning.
Explanation / Answer
You could use the example of addresses on numbered streets. For instance, Manhattan (new York City) has avenues running north-south and streets running east-west. An address of 1662 7th Ave. is between 16th & 17th on 7th avenue, which corresponds to coordinates (7, 16.62).
Most cities work with some version of an orthogonal plat such as this, although most have named streets instead of numbers. Still each street has an "address" of the form 200N (y=2) or 1500W (x = -15).
2) I have not heard of this in connection with functions.
If you have a set of ordered pairs is is a function if for each value of x there is
just one ordered pair (x,y).
3)
No, it doesn't matter.
The shape of the curve is determined by the equation. If its linear (of degree 1) then it will be purely a straight line, either sloping or down. If its of a higher degree like a quadratic or cubic equation, it will be concave in its appearance as you probably already know.
If no domain is precisely specified, you can use any value of x. It would be best to start at zero, and say go up to ten. You plot your two axes, insert the various values of x from 0 through 10, and plot the corresponding points.
An example, take a really, really, really easy function like y = 2x. You are choosing values of x to be 1, 2, 3,...,10. So get to work and see what this looks like. You know already it'll be linear, and positive. Or, you could plot just two points, substitute x = 2, and x = 10, plot the points and connect them with a single straight line.
You could also start with x = 14 and compute through x = 30 and the line will still be the same, because for every value of x, no matter what it is, y will be just two times the value of x.
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