Graph 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 an asymptote in the context of rational functions?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

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

Back

Vertical asymptotes occur at the values of x that make the denominator equal to zero, provided these values do not cancel with the numerator.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote describes the behavior of the function as x approaches infinity. It can be found by comparing the degrees of the numerator and denominator.

Front

What is the significance of a hole in the graph of a rational function?

Back

A hole occurs in the graph where a factor in the numerator and denominator cancels out, indicating that the function is undefined at that point.

Front

How do you determine the domain of a rational function?

Back

The domain of a rational function includes all real numbers except for the values that make the denominator zero.

Front

What transformations can be applied to the graph of a rational function?

Back

Transformations include vertical and horizontal shifts, reflections, and stretches or compressions.

Front

What is the effect of adding a constant to the numerator of a rational function?

Back

Adding a constant to the numerator shifts the graph vertically.

Front

What is the effect of multiplying the numerator by a constant?

Back

Multiplying the numerator by a constant stretches or compresses the graph vertically.

Front

What happens to the graph of a rational function when the denominator is multiplied by a constant?

Back

Multiplying the denominator by a constant stretches or compresses the graph horizontally.