Graphing Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Front

What is a vertical asymptote?

Back

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

Front

How do you find vertical asymptotes of a rational function?

Back

Set the denominator equal to zero and solve for x.

Front

What does it mean for a function to be reflected over the x-axis?

Back

It means that for every point (x, y) on the graph, the point (x, -y) is also on the graph.

Front

What does it mean for a function to be reflected over the y-axis?

Back

It means that for every point (x, y) on the graph, the point (-x, y) is also on the graph.

Front

What is a horizontal asymptote?

Back

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

Front

How do you find horizontal asymptotes of a rational function?

Back

Compare the degrees of the numerator and denominator polynomials.

Front

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

Back

Holes occur at values of x that make both the numerator and denominator zero, indicating a removable discontinuity.

Front

What is the transformation of the function y = f(x) + k?

Back

The graph of the function is shifted vertically by k units.

Front

What is the transformation of the function y = f(x - h)?

Back

The graph of the function is shifted horizontally by h units.