Name: ______________________________ Period: ______________

Unit 1 Functions and Their Inverse Review Packet

Do Now Space: Part 1: The list of questions covers all the materials we have learned in Unit 1. Please use your previous notes to answer the following questions.

1. When Do We Classify a Relation as a Function?

a. When each _____________ has only one ___________ value

b. Looking at a graph, when it passes _______________________________ (or VLT)

c. Looking at a map, if there is only one ________ coming from any _________ value

2. What does it mean for a value to be a Root, Minimum, or Maximum of a function?

a. Root is any point where a function touches the ____________.

b. Root has the same meaning as ____________ and _______________.

c. Minimum is the _______________ on a graph and maximum is the __________________ on a graph.

Determine the roots, minimum and/or maximum point of the graph.

Roots: ___________________ Minimum:_________________ Maximum: __________________

3. What does it mean for a function to be Concave Up or Down? (Draw an example of a graph when its function is concave up or concave down.)

4. What does an Inverse Function look like on a graph?

a. It reflects each point contained in the function over the line _____________.

b. In order to find points, you have to flip each point’s ____ and _____ coordinate.

c. In order to find an inverse function, you have to

i. First, switch ____ and ____ variables in your equation. ii. Second, _________________________.

Example: Find the inverse function for the following functions: !(#) = 2#' − 8 * # = { −2,3 , 0,5 , 2, −7 , 11,0 }

5. How do we use Operations like Addition and Subtraction? a. There are two methods:

i. Method 1: :5 6 + 8(6) in words, evaluate each function for x, then add the results.

ii. Method 2: : (5 + 8)(6) In words, _______ the functions, then ____________ the resulting function for x.

Example: Given f(x) and g(x), evaluate the expression when x = 2. ! # = 3# − 4

* # = #' − # + 6 Method 1: ! 2 + *(2) Method 2: (! + *)(2)

6. How do we find Composition of Functions?

a. Notation: !(* # ) =____________________ Example: Evaluate (! ∘ *)(2), when ! # = #' − 5 and * # = 2# + 7.

7. How do we know what Transformations are taking place without graphing the equation? Compare < = 6= and < = >(6 − ?)= + @

a. If a > 1, the graph is ________________.

b. If 0 < a < 1, the graph is ________________.

c. If a is negative, the graph is _____________________________________.

d. As d increases, the graph ___________________________.

e. As c increases, the graph ___________________________.

Example: Describe the transformations from < = |6| and < = −= 6 − B + CC

Part II: The following problems are Regents Exam Practice Problems. The Unit test will be similar to this format, so please treat it as if you are taking a test. 1. 2. 3. 4. 5.

6. 7. 8.

10.

11. 12. 13.

14. If ! # = D' # − 3 and * # = 2#' + 5,

a) What is the value of ! * −1 ? b) What is the value of ! ∘ * 2 ?

15. How does the graph of ! # = 3 # − 2 compare to the graph of * # = |#|? 16. Given the following functions,

! # = 3# + 8 * # = 3#F − 1

ℎ(#) = {(−2, 4), (0, −1), (1, 17), (5, 3), (7, 1)}

a) Find !(−2) + *(3)

b) Find * ℎ ! −1

c) Find *HD # (meaning, find the inverse of *(#))