inverse functions Unit 1 Day 17

F-BF. B. 4: I can find the inverse of a linear function F-BF.B.4: I can find the inverse of a linear function. I can describe how the graph of a relation and the inverse are related.

Developing an understanding… Create a simple linear function, and write it down in your notes. What makes your equation a function? What makes your equation a linear function? What does this function really do? Absentee Students: Take Notes While Watching the Videos https://www.khanacademy.org/math/algebra2/manipulating-functions/introduction-to-inverses-of-functions/v/introduction-to-function-inverses

Choose an arbitrary number for x. Then substitute it in for x and solve. Think about this abstractly. There is a set of things that can be INPUTTED into this function. This is known as the __________ of a function. The function inputs the number 2 and outputs the number 8. The function inputs the number 3 and outputs the number 10. The function inputs the number 4 and outputs the number 12.

A relation is mapping of input values onto output values. The set of all things that can be inputted into this function is referred to as the DOMAIN. The set of all possible resulting values, after input values, is known as the RANGE. A relation is mapping of input values onto output values. DOMAIN RANGE 2 8 10 3 12 4 2 is being mapped by the function to 8. 3 is being mapped by the function to 10. 4 is being mapped by the function to 12.

Is there a way to go backwards? DOMAIN RANGE 2 8 10 3 12 4 8 is being mapped by the function to 2. 10 is being mapped by the function to 3. 12 is being mapped by the function to 4.

The inverse of a function will take us back by mapping the output values back to their original input values. DOMAIN RANGE 2 8 10 3 12 4 8 is being mapped by the function to 2. 10 is being mapped by the function to 3. 12 is being mapped by the function to 4.

Describe how the domain and range of the original relation and its inverse relation are related.

Describe how the domain and range of the original relation and its inverse relation are related. The domain of the inverse relation is the range of the original relation, and the range of the inverse relation is the domain of the original relation.

How can we find the inverse relation algebraically?

Step 1 – Stick “y” in for “f(x)”.

Step 2 – Switch “x” and “y”.

Step 3 – Solve for “y”.

Step 4 – Replace the “y” with the inverse relation notation .

You can visually check your work by graphing and on the same graph.

Graph the original relation and the inverse relation using a graphing calculator.

Include the line .

The graphs of original relation and the inverse relation are reflections of one another across the green line y = x.

You can algebraically check your work by finding