The Range of a Function in Set Y

[kripkrip420]

Homework Statement

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Homework Equations

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The Attempt at a Solution

I guess I will start here. My question does not necessarily involve equations. In the Calculus book I am currently studying from, I am reviewing some pre-calculus and I came across a section that mentioned the range of the function does not have to be the entire Set Y. Now, what I was wondering was what exactly this means. Here are my thoughts.

Let's say you have a function f(x)=(x)/(x+1)

This function has a vertical asymptote at x=(-1)

This function also approaches a y-value y=1.

I am assuming that when the Calculus book said that the range doesn't always include every element in a Set Y, this is something like what they were referring to. Even thought the function doesn't ever get to y=1, that doesn't mean that y=1 is not included in the Set Y, correct? y=1 is still present in the Set Y even though the functions range does not include it. Am I correct in saying this? Also, x=(-1) is NOT in the domain of x correct? This is because the domain is defined as the Set D of all POSSIBLE input values. The Set Y is all the real numbers that extend through the real line y, whereas, the range is simply the output values of the function that may or may not include all the elements of the Set Y. Am I correct in what I have said so far?

Thank you very much in advance to everyone who has taken their time to answer my simple question!

 

[micromass]

Yes, this is entirely correct!

 

[kripkrip420]

Wow. Thank you for the lightning fast response! Also, I forgot to mention... Merry Christmas to you if you celebrate it and Merry Christmas to everyone else that celebrates it as well! Happy New Year!