Rational Functions and Their Properties

This video tutorial covers the properties of rational functions, including their definition, domain, and how to find the domain using set builder and interval notation. It explains the significance of zeros in the numerator and denominator, identifying x-intercepts and vertical asymptotes. The tutorial also provides guidance on graphing rational functions, emphasizing the behavior of graphs near asymptotes.

What is a rational function?

• A function that is always positive

• A function that is the ratio of two polynomials

• A function that has no variables

• A function that is always negative

What is the domain of a rational function?

• All real numbers except where the denominator is zero

• All real numbers

• All positive numbers

• All negative numbers

How do you find the domain of a rational function?

• Set both numerator and denominator equal to zero

• Set the function equal to zero

• Set the denominator equal to zero

• Set the numerator equal to zero

In set builder notation, how is the domain expressed?

• X such that X equals a specific value

• X such that X cannot equal a specific value

• X such that X is greater than a specific value

• X such that X is less than a specific value

What does it mean for a rational function to be in lowest terms?

• The denominator is zero

• The function is undefined

• The numerator is zero

• The numerator and denominator have no common factors

What do the zeros of the numerator represent?

• The y-intercepts

• The x-intercepts

• The vertical asymptotes

• The horizontal asymptotes

What do the zeros of the denominator represent?

• The horizontal asymptotes

• The vertical asymptotes

• The x-intercepts

• The y-intercepts

What is a vertical asymptote?

• A point where the graph intersects the x-axis

• A horizontal line the graph approaches

• A vertical line the graph approaches but never touches

• A diagonal line the graph crosses

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

• Set the function equal to zero

• Set the denominator equal to zero

• Set the numerator equal to zero

• Set both numerator and denominator equal to zero

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

• Set the denominator equal to zero

• Set the function equal to zero

• Set the numerator equal to zero

• Set both numerator and denominator equal to zero