2. Relations are a pairing of input and output values. You could say a list of points.

3. Functions pass the vertical line test. They have only one y-value for each x-value.

4. B A C How do you know?

5. Starburst Hershey’s 1 3 5 2 4 6 Skittles Snickers Reese’s Input Output Notice there is more than one output value for the input values of 1 and of 2. ( Vertical Line Test)

6. Starburst Hershey’s 1 3 5 2 4 6 Skittle s Snicker s Reese’s Input Output Starburst Hershey’ s 1 3 5 2 4 6 Skittles Snickers Reese’s Input Output How do you know? AB

7. The inverse has all of the x’s and y’s reversed.

8. f(x) = {(-2,0),(-1,3),(0,6),(1,0),(2,12)} Find f -1 (x) f -1 (x) = {(0,-2), (3,-1),(6,0),(0,1),(12,2)} Is the inverse a function? The -1 means the inverse of f(x) NO

9. 1) y = 2x + 3 What should we do to find the inverse? Exchange the x & y values x = 2y + 3 Isolate the “y”. 2y = x – 3 Is the inverse a function? YES If the original problem is “linear” then the inverse is linear. Both are functions.

10. 2) y = 6 Exchange the x & y values x = 6 Is the inverse a function? NO, because it is a vertical line. Write your answer like this: The inverse is x = 6 When the original problem is a horizontal line (yes a function) the inverse is a vertical line (not a function).

12. 4) y = x 2 + 4 Find the inverse NEW shape: We are starting with a quadratic function. Original problem “is” a function. Inverse “is NOT” a function.

13.  Plus or minus a square root function.

14. 4) y = x 2 + 4 Was the inverse a function? Would the original problem have passed a horizontal line test? Then the inverse will not pass a vertical line test. NOT a function. NO

15.  y = 2x – 4  y = 9  y = x 2 - 5 Would the given problem pass a horizontal line test? Will the inverse be a function?

16. The inverse on a graph is reflected across the line y = x Or you could say a 45 0 angle with the x-axis. HOW did I do that so quickly? List critical points and switch the x and y.

17. 1) Pick “critical points” on the given graph. 2) Switch the x and y values. 3) Sketch the new graph, in order. 4) Fold your paper to be sure you are correct.

19. Know the difference between relations and functions. Be able to find the inverse of a set of points (ordered pairs). Be able to take a linear or quadratic function and algebraically find the inverse. Be able to draw the inverse of a graph.

20. Does every function have an inverse? Is the inverse of every function also a function? What shape is the inverse of a quadratic function? What shape is the inverse of a linear function? What does the vertical line test tell you? What does the horizontal line test tell you?

21. WS