Graphing Rational expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Front

What is the domain of a rational expression?

Back

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

Front

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

Back

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

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches.

Front

What are vertical asymptotes?

Back

Vertical asymptotes occur where the denominator of a rational expression is zero.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes describe the behavior of a function as x approaches infinity or negative infinity.

Front

How do you determine the horizontal asymptote of a rational function?

Back

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, y=0; if equal, y= leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What is the significance of the x-intercept in graphing?

Back

The x-intercept indicates where the graph crosses the x-axis, showing the values of x for which the function equals zero.

Front

What is the significance of the y-intercept in graphing?

Back

The y-intercept indicates where the graph crosses the y-axis, showing the value of the function when x=0.

Front

How do you graph a rational function?

Back

Identify intercepts, asymptotes, and test points in each interval to sketch the graph.