Graphing Rational Functions: Vocab and Holes Insights

This video tutorial covers graphing rational functions, focusing on identifying holes, vertical and horizontal asymptotes, and determining domain and range. It explains graph transformations using simple equations, analyzes examples with positive and negative numerators, and discusses general rational functions and their restrictions. The tutorial also introduces the concept of holes and horizontal asymptotes, providing steps to find holes in graphs.

What does the numerator represent in the transformation of a rational function?

• X value

• H value

• A value

• K value

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

• Use the leading coefficient

• Set the numerator equal to zero

• Set the denominator equal to zero

• Find the highest exponent

If the K value is -1, what is the horizontal asymptote?

• Y = 1

• Y = -1

• X = -1

• X = 1

What happens to the graph when the numerator is negative?

• It shrinks horizontally

• It stretches vertically

• It moves to the right

• It reflects over the horizontal asymptote

In the second example, what is the vertical asymptote?

• X = -1

• X = 1

• Y = 1

• Y = -1

What is the general form of a rational function?

• A polynomial function

• A linear function

• One function over another function

• A quadratic function

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

• Set the denominator equal to zero

• Set the numerator equal to zero

• Find the highest exponent

• Use the leading coefficient

What is a hole in a rational function?

• A point where the graph intersects the x-axis

• A point where the graph intersects the y-axis

• A point where the numerator and denominator have the same zero

• A point where the graph intersects the asymptote

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

• Y = 1

• Y = 0

• X = 0

• X = 1

What is the horizontal asymptote when the degrees of the numerator and denominator are the same?

• Y = 0

• Y = the leading coefficient of the numerator

• Y = the leading coefficient of the denominator

• Y = the ratio of the leading coefficients