Graph Rational Functions Review

Front

What is the Horizontal Asymptote?

Back

The Horizontal Asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity. For rational functions, it can often be determined by the degrees of the numerator and denominator.

Front

What is the Vertical Asymptote?

Back

The Vertical Asymptote is a vertical line that the graph of a function approaches as the function's value approaches infinity or negative infinity. It occurs at values of x that make the denominator zero, provided the numerator is not also zero at that point.

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs at a point where a function is not defined due to a factor in the denominator that can be canceled with a factor in the numerator. This results in a 'hole' in the graph.

Front

How do you find the Y-Intercept of a rational function?

Back

To find the Y-Intercept, substitute x = 0 into the function and solve for y. The Y-Intercept is the point where the graph crosses the Y-axis.

Front

What is the significance of the degrees of the numerator and denominator in rational functions?

Back

The degrees of the numerator and denominator help determine the behavior of the function as x approaches infinity, including the existence and location of horizontal asymptotes.

Front

What is the ordered pair for the Y-Intercept of the function f(x) = (x^2 - 1)/(x - 2)?

Back

The ordered pair for the Y-Intercept is (0, -0.5).

Front

How do you determine the coordinates of a hole in a rational function?

Back

To determine the coordinates of a hole, factor both the numerator and denominator, identify the common factors, and set them equal to zero. The x-value of the hole is where the common factor equals zero.

Front

What is the formula for finding the Horizontal Asymptote when the degrees of the numerator and denominator are equal?

Back

When the degrees of the numerator and denominator are equal, the Horizontal Asymptote is found by dividing the leading coefficients of the numerator and denominator.

Front

What happens to the graph of a rational function at a Vertical Asymptote?

Back

At a Vertical Asymptote, the graph of the function approaches infinity or negative infinity, indicating that the function is undefined at that x-value.

Front

What is the difference between a hole and a vertical asymptote?

Back

A hole occurs when a factor cancels out in the function, while a vertical asymptote occurs when the function approaches infinity due to a zero in the denominator that does not cancel.