Graphing General Rational Functions

The video tutorial covers graphing general rational functions, focusing on understanding polynomial degrees, identifying zeros, vertical and horizontal asymptotes, and graphing techniques. It provides examples to illustrate how to graph rational functions with different characteristics, such as having no zeros or vertical asymptotes, and those with vertical asymptotes. The tutorial emphasizes the importance of understanding the degree of polynomials and how it affects the graph's horizontal asymptotes.

What is the degree of the polynomial (x^2 + 3x + 1)?

• 4

• 1

• 2

• 3

In the polynomial (x + x^2 + x^4), what is the highest degree?

• 3

• 1

• 4

• 2

What is a rational function composed of?

• A numerator and a denominator

• Only a numerator

• Only a denominator

• None of the above

What should you do if the numerator and denominator of a rational function have common factors?

• Multiply them

• Add them

• Subtract them

• Cancel them

How do you find the zeros of a rational function?

• Set the numerator equal to zero

• None of the above

• Set the denominator equal to zero

• Set both numerator and denominator equal to zero

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

• Set the numerator equal to zero

• None of the above

• Set the denominator equal to zero

• Set both numerator and denominator equal to zero

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

• No horizontal asymptote

• y = 0

• y = 1

• y = a/b

If the degrees of the numerator and denominator are equal, what is the horizontal asymptote?

• y = 0

• y = 1

• y = a/b

• No horizontal asymptote

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

• y = 0

• y = 1

• y = a/b

• No horizontal asymptote

When graphing a rational function, which characteristics should you analyze?

• Vertical asymptotes

• All of the above

• Zeros

• Horizontal asymptotes