Rational functions

Reciprocal functions, quadratic denominators, graphs of rational linear functions

Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)

Exercises

No exercises available for this concept.

SL AA 2.8

The reciprocal function is defined by f(x)=x1.

Notice that f(x) is not defined for x=0. In fact, since x1 gets very large as x approaches 0, f(x) has a vertical asymptote at x=0.

And since for very large x, x1 approaches zero, there is also a horizontal asymptote y=0.

Notice also that x11=x, so f(x)=x1 is self-inverse.

Powered by Desmos

SL AA 2.8

A linear rational function has the form

f(x)=cx+dax+b

When the denominator is zero the graph will have a vertical asymptote:

cx+d=0⇒x=−cd🚫

And as x gets very large, the +b and +d can be ignored:

y=f(x)≈cxax=ca🚫

So there is a horizontal asymptote at y=ca.

Powered by Desmos

SL AA 2.8

The reciprocal function is defined by f(x)=x1.

Notice that f(x) is not defined for x=0. In fact, since x1 gets very large as x approaches 0, f(x) has a vertical asymptote at x=0.

And since for very large x, x1 approaches zero, there is also a horizontal asymptote y=0.

Notice also that x11=x, so f(x)=x1 is self-inverse.

Powered by Desmos

SL AA 2.8

A linear rational function has the form

f(x)=cx+dax+b

When the denominator is zero the graph will have a vertical asymptote:

cx+d=0⇒x=−cd🚫

And as x gets very large, the +b and +d can be ignored:

y=f(x)≈cxax=ca🚫

So there is a horizontal asymptote at y=ca.

Powered by Desmos