Graphing the Inverse (5.1.4)

Question 1

• The horizontal line test says that if any horizontal line intersects the graph of a function at most once, then the function is one-to-one and is invertible.

Answer 1

• The horizontal line test says that if any horizontal line intersects the graph of a function at most once, then the function is one-to-one and is invertible.

Question 2

• The graph of the inverse of a function is the reflection of a one-to-one function’s graph across the line y = x.

Answer 2

• The graph of the inverse of a function is the reflection of a one-to-one function’s graph across the line y = x.

Question 3

• To reflect the graph of a function f across the line y = x, first identify several points on the graph of f and then reverse the coordinates of each point. The resulting points will each lie on the reflection of f across the line y = x. For example, if (a, b) is a point on the graph of f, then (b, a) is a point on the reflection across the line y = x. It follows that if (a, b) is a point on the graph of f and f is a one-to-one function, then (b, a) is a point on the graph of the inverse of f.

Answer 3

• To reflect the graph of a function f across the line y = x, first identify several points on the graph of f and then reverse the coordinates of each point. The resulting points will each lie on the reflection of f across the line y = x. For example, if (a, b) is a point on the graph of f, then (b, a) is a point on the reflection across the line y = x. It follows that if (a, b) is a point on the graph of f and f is a one-to-one function, then (b, a) is a point on the graph of the inverse of f.