Unit 5.4 SMC: Graphing 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.

Front

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

Back

To find the coordinates of a hole, set the common factors in the numerator and denominator to zero and solve for x, then substitute back to find y.

Front

What is a horizontal asymptote?

Back

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

Front

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

Back

Compare the degrees of the numerator and denominator: if the degree of the numerator is less, the asymptote is y=0; if they are equal, divide the leading coefficients; if the numerator's degree is greater, there is no horizontal asymptote.

Front

What is the domain of a rational function?

Back

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

Front

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

Back

To find the vertical asymptote, set the denominator equal to zero and solve for x.

Front

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

Back

A hole indicates a point where the function is not defined due to a common factor in the numerator and denominator.

Front

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

Back

A hole occurs at a point where the function is undefined due to a removable discontinuity, while a vertical asymptote indicates a point where the function approaches infinity.

Front

What does it mean for a function to approach an asymptote?

Back

It means that as the input values get very large or very small, the output values get closer and closer to the value of the asymptote.

Front

What is the range of a rational function?

Back

The range of a rational function is the set of all possible output values, which can be determined by analyzing the function's behavior and asymptotes.