Presentation on theme: "Inverses of Functions Part 2 Lesson 2.9. Reminder from yesterday."— Presentation transcript:
Inverses of Functions Part 2 Lesson 2.9
Reminder from yesterday
Vertical Lines Choose 4 points on the vertical line below. Write the coordinates for each. What IS a vertical line? A line composed of all the points _________________. with the same x value
Vertical Line Rule Why do we use a vertical line to determine if a graph is a function? If a vertical line passes through 2 points on a graph, both those points have the same ____ value but 2 different ___ values. Therefore, the ______ has _______________ output. This means the graph _____ a function. In a function, each x value has ________ y value. x y only one input more than one is not
Practice What does this tell you about this graph? Why does the vertical line rule determine if a graph is a function?
Is the Inverse of the Function a Function? Draw the inverse of the function below. Use the vertical line rule to determine if the inverse of f is a function.
The horizontal line rule Horizontal line in the original becomes a vertical line in the inverse:
The horizontal line rule (cont’d) If a horizontal line drawn through ______________ crosses more than one point, _______________ is not a function. At these two points, the graph of the original has one ____________ with multiple ______________. So, its inverse will have one ________ with multiple _________ the original graph its inverse output inputs input outputs
Horizontal v. Vertical Line Test Use vertical line test when we have the graph of the inverse Use horizontal line test when we only have the graph of the original function, and not the inverse
Practice 1. Determine whether the following graphs are functions. 2. WITHOUT drawing the inverse graph, determine whether the inverse of the relation is a function. function not a function
Defend your answer Graph the inverse. Use the vertical line rule.
Independent Practice Complete Problem Set independently.