1. Reflection 4.1
Let’s do a Reflection. Tell me...
3 new things you have learned this school year
2 connections you have made with your learning this school year (either between classes or between class and the “real world”)
1 thing that you would like to learn more about before the year is over

2. USING COMPOSITE FUNCTIONS (S5.1)
Unit 4: Analyze Exponential and Logarithmic Functions
Target 4.1, Day 1
USING COMPOSITE FUNCTIONS (S5.1)

3. Recall that function __________________ is an operation in which you plug the answer from one function into another function (or plug an entire function into another function). Think of it as “substitution” from back in the substitution/elimination days.
We’ve already seen function composition look like this…
Say, “f of g of x”
Now we are going to see it look like this…
Say, “f composed with g of x”
They are the same thing! You say potato, I say pah-TAH-toe…

4. Evaluate the indicated composite function.

5. Find the indicated composite function.

6. To find the domain of a composite function, first consider the domain of the “______________” function. Then consider the domain of the ______________ function.
Find the domain of the indicated composite function.

7. Find the indicated composite function. Then find its domain.

8. Find the indicated composite function. Then find its domain.

9. Warm Up 4.1, Day 2
Evaluate the indicated composite function.
Find the indicated composite function. Then find its domain.

10. USING INVERSE FUNCTIONS (S5.2)
Unit 4: Analyze Exponential and Logarithmic Functions
Target 4.1, Day 2
USING INVERSE FUNCTIONS (S5.2)

11. An inverse function is created by switching the _____________ and _____________ of a function.
Find the inverse of
Graph the original function and its inverse on the same graph. Also, graph the line y = x. What do you notice?

12. Sketch a graph of Do you recall the name of the test that can tell you whether or not the graph represents a function?
Next, sketch its inverse by reflecting the graph over the line y = x. Is the inverse a function?
The Horizontal Line Test states that the ______________ of a function is also a function if and only if any horizontal line intersects the _____________ graph once.
VLT  Use it on the original, tells you if the ________ is a function
HLT  Use it on the original, tells you if the ________ is a function

13. Can you sketch a graph that is not a function but whose inverse is?
What about a graph that is not a function and whose inverse is also not a function?
What about a graph that is a function and whose inverse is also a function?

14. If the graph of a function passes the HLT, we can also say that the function is __________________________ meaning that no two inputs go to the ___________ output.
Determine if the function is one-to-one. Explain.
Decide if the mapping diagram shows a function. If it does, is it a one-to-one function?

15. Verify that the function is one-to-one. Then find the inverse.

16. Verify that the function is one-to-one. Then find the inverse.