Rational Graphing

How do you find a hole?

A hole comes when a factor is in the numerator and denominator and you cross it out. It is the x value that makes the factor equal zero.

What is a horizontal asymptote?

A horizontal line the graph approaches on both ends of a graph. It is the end behavior of a graph.

What is a vertical asymptote?

A vertical line a rational graph approaches, but never crosses.

How do you find x-intercepts?

After simplifying the function, you set the numerator equal to zero and solve for x (find values of x that make the numerator equal 0)

How do you find a vertical asymptote?

After you simplify your function, your vertical asymptotes are values of x that make the denominator equal zero.

How do you write a hole?

As a point or ordered pair (x, y). You find the x value of the hole and plug it back into the simplified equation to get the y - value.

How do you write a vertical asymptote?

As an equation x = a

How do you write a horizontal asymptote?

As an equation y = a

How do you find domain restrictions?

Factor the denominator. They are any value that makes the denominator equal zero because we can't divide by zero.

How do you write domain restrictions?

x ≠ a

What is the horizontal asymptote if the degree of the numerator is less than the degree of the denominator?

y = 0

What is the horizontal asymptote if the degree of the numerator equals the degree of the denominator?

y = coefficients. You find the leading coefficient of the numerator and divide it by the leading coefficient of the denominator.

What is the always the first step of solving or graphing a rational function?

To factor!!

How do you find y-intercepts?

Plug zero in for x in your equation and simplify.

What is the horizontal asymptote if the degree of the numerator is more than the degree of the denominator?

There is no horizontal asymptote

How do you find a horizontal asymptote?

You compare the degree of the numerator to the degree of the denominator.