Transformations of Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is the general form of a rational function?

Back

The general form of a rational function is f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials.

Front

What does it mean for a function to have a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find the vertical asymptotes of a rational function?

Back

Vertical asymptotes can be found by setting the denominator Q(x) = 0 and solving for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the function approaches as x approaches infinity or negative infinity.

Front

How do you determine the horizontal asymptote of a rational function?

Back

The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator polynomials.

Front

What effect does the transformation f(x) = f(x - h) have on the graph of a function?

Back

The transformation f(x) = f(x - h) shifts the graph of the function to the right by h units.

Front

What effect does the transformation f(x) = f(x) + k have on the graph of a function?

Back

The transformation f(x) = f(x) + k shifts the graph of the function up by k units.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero.

Front

What is the range of a rational function?

Back

The range of a rational function is all real numbers except for the values that the function approaches but never reaches, often related to horizontal asymptotes.