Rational Function Graphs

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials and Q(x) ≠ 0.

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

How do vertical asymptotes relate to rational functions?

Back

Vertical asymptotes occur at the values of x that make the denominator of a rational function equal to zero.

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 find horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator: If degree of numerator < degree of denominator, y=0; if equal, y= leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What is the effect of adding a constant to a rational function?

Back

Adding a constant to a rational function shifts the graph vertically. For example, f(x) = P(x)/Q(x) + k shifts the graph up by k units.

Front

What does the transformation f(x) = f(x - h) represent?

Back

The transformation f(x) = f(x - h) represents a horizontal shift of the graph to the right by h units.

Front

What is the significance of the x-intercept in a rational function?

Back

The x-intercept of a rational function is the value of x where the function equals zero, found by setting the numerator equal to zero.

Front

What is the significance of the y-intercept in a rational function?

Back

The y-intercept of a rational function is the value of the function when x = 0, found by evaluating f(0) = P(0)/Q(0).

Front

How does the graph of f(x) = 1/x differ from f(x) = 1/(x - h)?

Back

The graph of f(x) = 1/(x - h) is a horizontal shift of f(x) = 1/x to the right by h units.