- #1
Why Is the Radius (1-x) Instead of (1+x)?
- Thread starter Miike012
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Homework Help Overview
The discussion revolves around the interpretation of the radius in a mathematical context, specifically questioning why it is represented as (1 - x) instead of (1 + x). Participants are examining the implications of this representation in relation to a graph of an exponential curve.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants are exploring the reasoning behind the choice of (1 - x) and questioning the labeling of points on the graph. There is also a discussion about the generalization of coordinate labeling across different quadrants.
Discussion Status
Some participants have provided clarifications regarding the distance from points on the curve to the line x = 1, while others are questioning the assumptions made about the signs of variables in different quadrants. There is an ongoing exploration of the concepts without a clear consensus yet.
Contextual Notes
Participants are working with visual aids, such as images, to support their reasoning, but there are issues with clarity in some of these materials. The discussion also touches on the conventions of labeling coordinates in various quadrants.
- #2
Mark44
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Your image is too faint for me to read.Miike012 said:
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- #4
Mark44
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Much better - thanks!
The horizontal distance from a point (x, y) on your exponential curve to the line x = 1 is 1 - x. For most of the interval [-1, 0], the x values are negative, so this distance will generally be larger than 1, but less than 2.
Also, the point is labelled incorrectly. It should be (x, f(x)), not (-x, f(-x)).
The horizontal distance from a point (x, y) on your exponential curve to the line x = 1 is 1 - x. For most of the interval [-1, 0], the x values are negative, so this distance will generally be larger than 1, but less than 2.
Also, the point is labelled incorrectly. It should be (x, f(x)), not (-x, f(-x)).
- #5
Miike012
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it should be (x,f(x)) even though its in the 2nd quad? is this general for all quad that x and f(x) be positive when labeling an arbitrary coordinate ?
- #6
Mark44
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Yes.Miike012 said:
You are assuming that x is always positive and -x is always negative - no, this isn't true. You can't tell the sign of a variable by whether it has a + or - in front of it. For example, -b could be positive or negative, depending on the value of b. Similarly, +c could be positive or negative, depending on the value of c. Note that we don't normally write +c, but I'm just trying to make a point.Miike012 said:
Think about the x-axis. If x is a number to the left of zero, it's negative. We DO NOT write this as -x.
- #7
Miike012
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Thank you so much that really helps.
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