BIG IDEAS MATH - Skills Review Notes

BIG IDEAS MATH

#7

Skills Review: Using Tools

• Objective: To determine whether the inverse of a function f is itself a function.

• Methodology:

  • Utilize the graph of the function f.
  • Apply the Horizontal Line Test:
  • A function f has an inverse that is also a function if and only if every horizontal line crosses the graph of f at most once.

Explanation of the Horizontal Line Test

• Definition: The Horizontal Line Test is a method used to determine if a function is one-to-one.
• Criteria:
  • If any horizontal line intersects the graph of the function more than once, the inverse is not a function.
  • If all horizontal lines intersect the graph no more than once, then the inverse of the original function is a function.

Application to the Given Problem

• Examine the graph of f:
  • Determine where horizontal lines intersect the graph.
  • Analyze those intersections to conclude whether the inverse is also a function.