Horizontal asymptote of a reciprocal function

[fred2028]

This isn't something that grade 11s are required to know but grade 12s are, so I will learn ahead.

I know how to find the vertical asymptotes from a reciprocal function equation, but how do you find the horizontal asymptote?

 

[stapel]

What do you mean by a "reciprocal" function?

Are you requesting lessons on this topic?

Thank you.

Eliz.

 

[fred2028]

What do you mean by a "reciprocal" function?

Are you requesting lessons on this topic?

By reciprocal function I mean reciprocal of say a linear equation, y=mx+b, where there 2 asymptotes and 2 graphs.

 

[stapel]

By reciprocal function I mean reciprocal of say a linear equation, y=mx+b, where there 2 asymptotes and 2 graphs.

Okay, but what do you mean by "reciprocal"? Are you saying that, given f(x) = mx + b, the "reciprocal" is g(x) = 1/(mx + b)? So you're asking about one particular type of rational function...?

Note: The g(x) shown above has only one graph (I'm not sure what you mean by one function somehow having two graphs), and only one vertical asymptote. Were you perhaps referring also to the horizontal asymptote...?

Thank you.

Eliz.

 

[fred2028]

By reciprocal function I mean reciprocal of say a linear equation, y=mx+b, where there 2 asymptotes and 2 graphs.

Okay, but what do you mean by "reciprocal"? Are you saying that, given f(x) = mx + b, the "reciprocal" is g(x) = 1/(mx + b)? So you're asking about one particular type of rational function...?

Note: The g(x) shown above has only one graph (I'm not sure what you mean by one function somehow having two graphs), and only one vertical asymptote. Were you perhaps referring also to the horizontal asymptote...?

Thank you.

Eliz.

Well by reciprocal I mean f(x)=ym+b --> f^-1(x)=1/(mx+b). By 2 graphs I meant the curve in the 1st and third quadrants, the 2 curves which do not meet ...

 

[stapel]

The notation "f^-1(x)" has a specific meaning: the inverse function of f(x). It is not the reciprocal of the function, 1/(f(x)).

In any case, the function 1/(mx + b) is just a very simple rational function. So, to learn about the various techniques for finding asymptotes, intercepts, and graphs, do a search for information on graphing rational functions.

Eliz.