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Graphing Inverses. Objectives. I can graph the inverse of a relation from another graph. CONCEPT OF AN INVERSE FUNCTION. Idea : An inverse switches the Input and Output of a relation to form the new inverse Note that this really says that the roles of x and y are reversed.

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Presentation Transcript
objectives
Objectives
  • I can graph the inverse of a relation from another graph
concept of an inverse function
CONCEPT OF AN INVERSE FUNCTION

Idea: An inverse switches the Input and Output of a relation to form the new inverse

Note that this really says that the roles of x and y are reversed.

notation for the inverse function
NOTATION FOR THE INVERSE FUNCTION

We use the notation

for the inverse of f(x).

NOTE:

does NOT mean

graphing an inverse function
GRAPHING ANINVERSE FUNCTION

Given the graph of a relation, the graph of its inverse is obtained by switching x- and y-coordinates.

The resulting graph is reflected about the line y = x.

what steps can you come up with to accurately graph the inverse
What steps can you come up with to accurately graph the inverse?

1) Pick “critical points” on the given graph.

2) Switch the x and y values.

3) Sketch the new graph.

4) Fold your paper to be sure you are correct.

example ordered pairs

Example: Find the graph of the inverse relation geometrically from the graph of f(x) =

y

2

The ordered pairs of f are given by the equation .

x

-2

2

The ordered pairs of the inverse are given by .

-2

The graphs of a relation and its inverse are reflections in the line y = x.

Example: Ordered Pairs

y = x

homework
Homework
  • WS 3-1