Rational Function Solutions

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

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

Back

To find the x-intercepts, set the numerator of the rational function equal to zero and solve for x.

Front

What is the process for adding rational expressions?

Back

To add rational expressions, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

Front

What is the process for subtracting rational expressions?

Back

To subtract rational expressions, find a common denominator, rewrite each expression with that denominator, and then subtract the numerators.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the algebraic process but does not satisfy the original equation.

Front

How do you check for extraneous solutions?

Back

Substitute the solution back into the original equation to see if it holds true.

Front

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

Back

The denominator cannot be zero, as this would make the function undefined.

Front

How do you solve a rational equation?

Back

To solve a rational equation, find a common denominator, eliminate the denominators, and solve the resulting polynomial equation.

Front

What is the formula for finding the least common denominator (LCD)?

Back

The least common denominator is the smallest multiple of the denominators of the rational expressions involved.

Front

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

Back

A rational function is undefined at values of x that make the denominator equal to zero.