THE MYSTERY OF.... Solving 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 the general form of a rational function?

Back

The general form is f(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials.

Front

What does it mean to solve a rational function?

Back

To solve a rational function means to find the values of x that make the function equal to zero or undefined.

Front

What is a vertical asymptote in a rational function?

Back

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

Front

What is a horizontal asymptote in a rational function?

Back

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

Front

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

Back

Set the numerator P(x) equal to zero and solve for x.

Front

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

Back

Evaluate the function at x = 0, i.e., find f(0).

Front

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

Back

The denominator determines where the function is undefined and can create vertical asymptotes.

Front

What is the process for simplifying a rational function?

Back

Factor both the numerator and denominator and cancel any common factors.

Front

What does it mean for a rational function to be undefined?

Back

A rational function is undefined when the denominator equals zero.