Rational Transformations

Front

What is a rational function?

Back

Front

What is the domain of a rational function?

Back

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

Front

What is a vertical asymptote?

Back

Front

What is a horizontal asymptote?

Back

Front

How do you find vertical asymptotes?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

How do you find horizontal asymptotes for rational functions?

Back

For rational functions, compare the degrees of the numerator and denominator: If degree of P < degree of Q, y = 0; if degree of P = degree of Q, y = leading coefficient of P / leading coefficient of Q; if degree of P > degree of Q, there is no horizontal asymptote.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator equals zero, leading to division by zero.

Front

What is a transformation in the context of functions?

Back

A transformation refers to changes made to the graph of a function, such as shifts, reflections, stretches, or compressions.

Front

What is a vertical shift?

Back

A vertical shift occurs when a constant is added to or subtracted from a function, moving the graph up or down.

Front

What is a horizontal shift?

Back

A horizontal shift occurs when a constant is added to or subtracted from the input of a function, moving the graph left or right.