Rational Transformations

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 parent function of a rational function?

Back

Front

What are asymptotes in rational functions?

Back

Asymptotes are lines that the graph of a function approaches but never touches. They can be vertical, horizontal, or oblique.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur where the denominator of a rational function is equal to zero.

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes are found by analyzing the degrees of the numerator and denominator polynomials.

Front

What is the significance of the horizontal asymptote?

Back

The horizontal asymptote indicates the behavior of the function as x approaches infinity or negative infinity.

Front

What does it mean for a function to be undefined?

Back

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

Front

What transformation occurs when a function is shifted up by 2 units?

Back

The transformation shifts the entire graph of the function vertically upwards by 2 units.

Front

What transformation occurs when a function is reflected over the x-axis?

Back

Reflecting a function over the x-axis inverts the y-values of the function.

Front

What is the effect of shifting a function left by 2 units?

Back

Shifting a function left by 2 units moves the entire graph horizontally to the left by 2 units.