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Inverse Graphs

Inverse Graphs. I nverse. The inverse of a relation is formed by interchanging the variables. Interchange to get inverse graph. Interchange x and y to get the inverse function and graph it along with the original relation. Answer. Interchange columns and plot on original graph. Tests.

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Inverse Graphs

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  1. Inverse Graphs

  2. Inverse • The inverse of a relation is formed by interchanging the variables.

  3. Interchange to get inverse graph • Interchange x and y to get the inverse function and graph it along with the original relation.

  4. Answer • Interchange columns and plot on original graph

  5. Tests • Inverses are reflections about the line y=x • The vertical line test is for determining whether a relation is a function. • The horizontal line test is for determining whether a relation has an inverse function.

  6. Functions and inverse functions • Are the following functions? Do they have inverse functions?

  7. Answer • Yes (passes vertical), no (fails horizontal) • Yes (passes vertical),yes (passes horizontal) • No (fails vertical), yes (passes horizontal)

  8. Verifying inverses • To verify that two relations are inverses of one another, compose each and get the identity x both times.

  9. Verifying • Verify that

  10. Answer • Compose both ways.

  11. To find an inverse • Switch the variables and solve for y

  12. Finding Inverses • Find the inverse of f(x)=3x-5.

  13. Answer • Switch x and y and solve for y.

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