Math 4 Unit 2: Functions and Their Graphs

Vocab

Domain – the span of all the x-values of a function

Range – the span of all the y-values of a function

x-intercept(s) – the point(s) where a function touches the x-axis

y-intercept – the point where a function touches the y-axis

Horizontal asymptote(s) – the imaginary line(s) where the domain of a rational function approaches on both sides but never touches.

• There are three rules that define where the asymptote will be and how it will look like:
  • If the degree of the numerator is less than the degree of the denominator, the asymptote will, by default, be y = 0.
    • The asymptote will be higher or lower if there is a k value in the function.
  • If the degree of the numerator is equal to the degree of the denominator, the asymptote will, by default, be at y = (degree of the numerator/degree of the denominator)
    • The asymptote will be higher or lower if there is a k value in the function.
  • If the degree of the numerator is greater than the degree of the denominator, there will not be a horizontal asymptote.

Vertical asymptote – the imaginary line(s) where the range of a rational function approaches above and below but never touches.

Local minimum – the point where a positive even polynomial’s vertex is, where the function does not go any lower.

Local maximum – the point where a negative even polynomial’s vertex is, where the function does not go any higher.

End behavior – the direction, attributes, and/or limit of a function as it goes left or right.