Inverses of Functions Part 2 Lesson 2.9

Reminder from yesterday Add to the cue column in your notes: When graphing the 𝑓 −1 𝑥 , choose points 𝑓(𝑥) on either side of the vertex

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. only one What kind of line did we draw here? What is occurring at the circled points? What do we know about the x values of these two points? What does that mean about whether the graph is a function? Stress RIGHT is RIGHT. x y input more than one is not only one

Practice Draw the line 𝑥=3 through the graph. Circle the points where it crosses the graph. Write the coordinates of those points. 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: 𝑦=−3 𝑥=−3

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 𝑦=−3 output inputs input outputs 𝑥=−3

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. WITHOUT drawing the inverse graph, determine whether the inverse of the relation is a function. Graph 3 - function 𝑓(𝑥) not a function function function 𝒇 −𝟏 (𝒙) function not a function function

Defend your answer Graph the inverse. Use the vertical line rule.

Independent Practice Complete Problem Set independently.