Why Is the Radius (1-x) Instead of (1+x)?

[Miike012]

My work is in the paint doc... my only question is... why is the radi 1-x and not 1+x?

My reason for why I think it is 1 - x is in the paint doc, please let me know why I am wrong.. thank you.

 

[Mark44]

My work is in the paint doc... my only question is... why is the radi 1-x and not 1+x?

My reason for why I think it is 1 - x is in the paint doc, please let me know why I am wrong.. thank you.

Your image is too faint for me to read.

 

[Miike012]

Try this image.

 

[Mark44]

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)).

 

[Miike012]

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 ?

 

[Mark44]

it should be (x,f(x)) even though its in the 2nd quad?

Yes.

is this general for all quad that x and f(x) be positive when labeling an arbitrary coordinate ?

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.

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.

 

[Miike012]

Thank you so much that really helps.