Rational Graphs Practice

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

Front

What is the domain of a rational function?

Back

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

Front

How do you find the vertical asymptote of a rational function?

Back

The vertical asymptote occurs at the values of x that make the denominator zero, provided the numerator is not also zero at those points.

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 determine the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, 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 is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, found by setting f(x) = 0.

Front

What is a y-intercept?

Back

A y-intercept is a point where the graph of a function crosses the y-axis, found by evaluating f(0).

Front

What does it mean for a function to shift left or right?

Back

A shift left means the graph moves to the left by a certain number of units, while a shift right means it moves to the right by that number of units.

Front

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

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