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**Inverses of Functions Part 2**

Lesson 2.9

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**Reminder from yesterday**

Add to the cue column in your notes: When graphing the π β1 π₯ , choose points π(π₯) on either side of the vertex

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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

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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

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**Practice Draw the line π₯=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?

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**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.

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**The horizontal line rule**

Horizontal line in the original becomes a vertical line in the inverse: π¦=β3 π₯=β3

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**The horizontal line rule (contβd)**

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 π¦=β3 output inputs input outputs π₯=β3

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**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

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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 π(π₯) not a function function function π βπ (π) function not a function function

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

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Independent Practice Complete Problem Set independently.

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