Bell Ringer 2-1-19 1. What is a function? 2. What are 2 ways to determine if a relation is a function? 3. What is domain? What is range? 4. What do “a”, “h”, and “k” do? ex: f(x) = a|x-h|+k

Week of inspirational math day 4

Inverse Functions Friday, February 1, 2019

Inverse Functions The basics: If it’s a table or a set of ordered pairs, simply switch x and y. If it’s a graph, the inverse is a reflection across the line y = x. If you have the function in y = or f(x) = form, switch x and y and solve for y.

Inverse Graphing Discovery

Classwork -- Find your Partner Follow the directions on your card to fill in your table. Find the classmate who has the inverse function. This is your partner. Introduce yourself and both of you see Mrs. Leahy. Glue down your tables on the paper Mrs. Leahy gives you. Remember to write your names on your paper. Label the table you glued on the left f (x). Label the table you glued on the right f -1 (x). Plot the points you have on your graph. Each of you should use a different color for your function. Determine the equation of your function. If you need help, see Mrs. Leahy. Complete the line or curve for your graphical representation of your function. Draw the line y = x. Are f (x) and f -1 (x) reflections over that line? If not, fix it. Classwork -- Find your Partner

Make the inverse Since we know visually functions and their inverses are reflections over the line y = x, we should realize that to create an inverse function, you switch x and y (from transformations in Math II. Based on that, create a table of the inverse of this function. Please use correct function notation for the inverse.

Graphing Graph 2 functions and the line y = x. If the graphs are reflections over the line y = x, then the functions are inverses of each other.

Algebraic Inverse Replace f(x) with y. Switch x and y. Solve for y. Replace y with f-1(x).

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

Here’s the graph of the function and its inverse Here’s the graph of the function and its inverse. You can check by graphing to see that the function and its inverse are reflected over the line y = x. http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

Here’s the graph of the function and its inverse Here’s the graph of the function and its inverse. You can check by graphing to see that the function and its inverse are reflected over the line y = x. http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

Inverse functions worksheet homework Inverse functions worksheet

exit ticket How do you determine the inverse of a table? How can you visually determine if two functions are inverses? What is the process for finding the algebraic inverse?