Understanding Rational Functions

In this video, the teacher introduces rational functions, explaining their properties and differences from reciprocal functions. The video covers steps to graph rational functions, including finding intercepts, vertical and horizontal asymptotes, and identifying holes. An example is provided to illustrate these concepts, along with determining the domain and range. The lesson concludes with plotting points to sketch the graph, emphasizing the similarities and differences between rational and reciprocal functions.

What distinguishes a rational function from a reciprocal function?

• A reciprocal function has a polynomial in the numerator.

• A rational function has a polynomial in the numerator and denominator.

• A rational function has only a number in the numerator.

• A reciprocal function has a polynomial in both the numerator and denominator.

What is the first step in graphing a rational function?

• Find the horizontal asymptote.

• Determine the domain.

• Simplify the function.

• Find the vertical asymptote.

How do you find the x-intercept of a rational function?

• Set the function equal to one.

• Set the numerator equal to zero.

• Set the denominator equal to zero.

• Set both numerator and denominator equal to zero.

What happens if the degree of the numerator is greater than the degree of the denominator?

• The horizontal asymptote is the x-axis.

• There is no horizontal asymptote.

• The horizontal asymptote is y = 1.

• There is a horizontal asymptote at y = 0.

When do holes occur in the graph of a rational function?

• When the degrees of numerator and denominator are equal.

• When the numerator is zero.

• When there is a common factor in the numerator and denominator.

• When the denominator is zero.

What is the vertical asymptote of the function if the denominator is x + 4?

• x = 4

• x = -4

• y = 4

• y = -4

How do you determine the horizontal asymptote when the degrees of the numerator and denominator are equal?

• It is the x-axis.

• It is the leading coefficient of the numerator divided by the leading coefficient of the denominator.

• There is no horizontal asymptote.

• It is y = 0.

What is the domain of a rational function with a vertical asymptote at x = -4?

• All real numbers except x = -4

• All real numbers except x = 0

• All real numbers except x = 4

• All real numbers

What is the range of a rational function with a horizontal asymptote at y = 1?

• All real numbers except y = 0

• All real numbers

• All real numbers except y = -1

• All real numbers except y = 1

What tool can be used to help plot points for graphing a rational function?

• A compass

• A graphing calculator

• A protractor

• A ruler