Approaching Graphing Rational Expressions

Front

If the degree of the numerator is greater than the degree of the denominator, what can be said about the horizontal asymptote?

Back

There is no horizontal asymptote.

Front

If the degree of the numerator is less than the degree of the denominator, what is the horizontal asymptote?

Back

The horizontal asymptote is y = 0.

Front

Simplify the expression: (x²+11x+24)/(x²+4x-32)

Back

(x+3)/(x-4)

Front

If the degree of the numerator is equal to the degree of the denominator, how is the horizontal asymptote determined?

Back

The horizontal asymptote is the lead coefficient of the numerator over the lead coefficient of the denominator.

Front

What is a rational expression?

Back

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

Front

What is the first step in graphing a rational expression?

Back

Identify the vertical asymptotes by setting the denominator equal to zero.

Front

What does it mean if a rational expression has a hole in its graph?

Back

A hole occurs when a factor in the numerator and denominator cancels out, indicating a point where the function is undefined.

Front

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

Back

Set the numerator equal to zero and solve for x.

Front

What is the significance of vertical asymptotes in the graph of a rational function?

Back

Vertical asymptotes indicate values of x where the function approaches infinity or negative infinity.

Front

What is the end behavior of a rational function?

Back

The end behavior describes how the function behaves as x approaches positive or negative infinity.