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Math 2: Algebra 2, Geometry and Statistics

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Inverse Functions Name: Date:

Finding Inverse Functions – Guided Notes

We’ve explored the idea that the inverse of a function undoes the function. One way of

finding the inverse of a function is to _______________________________________________________. You

can think of this as switching the inputs and the outputs.

Example 1: Find the inverse of a(b) = 3b – 7

Example 2: Find the inverse of a(b) = 3b3 – 2b + 5

Example 3: Find the inverse of a(b) = 2x2 + 3x + 4

But the function in example 3 is not _________________________ so even though we can find an

inverse, that inverse is not a function. We can solve this problem by _____________________

____________________________ of both the function and its inverse.

Math 2 Week 4 Packet




Similarly, we can also easily find the inverse of the graph of a function by switching the

inputs and the outputs. In graph form this looks like _____________________________________.

Example 4: Sketch the inverse of the graph shown below.


Is the inverse a function? Why or why not?

4

2

–2

–4

–5 5

4

2

–2

–4

–5 5







Generalize: To sketch the graph of the inverse of a function, reflect the graph of the

function across the line _________________________________. This will switch the inputs and the

outputs.

Groupwork: In your groups, read and complete the work in the textbook beginning

with #2 on page 301 and ending with #4 on page 304.

Homework: Pages 306-‐208 # 3, 4 (a-‐f) (use your calculator), 5, and 7. The following

problems are reach problems: 3c, 3e, 4e, and 4f. All the rest are standard problems.

4

2

–2

–4

–5 5

4

2

–2

–4

–5 5




Do Now 11.5 Name: Date:

Do Now 11.5 –Evaluating Functions

Consider the function f(x) = 3x3 – 2x2 + 5x – 4.

1. Find f(1)

2. Find f(2)

3. Find f(10)

4. Find f(f(3)

5. Find f-‐1(1444)

6. Find f-‐1(f-‐1(31082)

7. Find f(f(15)

8. Find f(20)




Do Now 12 Name: Date:

Do Now 12 – Inverses of Functions

1. Find inverse functions for these functions.

a.

€

k(x) =4(x + 6)3

− 2 b.

€

v(x) =15 − x4

2. Sketch the graph of the inverse of each function on the same axes. Determine whether the inverse is a function or merely a relation. a.

b.



4

2

–2

–4

–5 5

4

2

–2

–4

–5 5




Unit 1 Test Review Name: Date:

Unit 1 Test Review

Students will be able to (SWBAT):

• Write an explicit and a recursive function rule for a linear table of values.

• Describe in words or write a recursive function rule for a non-linear table of values.

• Determine whether a relation is a function based on a description, a table, or a graph.

• Find domain and range of a function from a graph.

• Based on an equation, determine domain restrictions for rational and radical functions.

• Find the inverse of a linear function.

• Given the graph of a linear function, graph its inverse.

• Evaluate compositions of functions, and find a rule for a composition.

1. Consider the functions f(x)=3x+7

g(x)=

€

x +12

Calculate each value

a. f(2) b. g(3) c. f(g(5)) d. g(f(2)) e.

€

f (2)⋅ g(3) f. f(2) + g(3)





2. Given the functions R(x) = x – 2 Q(x)=

€

x 2 + 4x +1 a. Find a formula for R(Q(x)) b. Find a formula for Q(R(x)) 3. State the domain of each function. You must write inequalities or use interval notation a.

€

b(x) = 2x 2 − 6 b.

€

c(x) = 2x − 6

Domain: Domain:

c.

€

d(x) =4

8 + x d.

€

e(x) =1+ x1+ x

Domain: Domain:





4. State the domain and range of each function. The functions do NOT extend beyond the graphs shown.. a.

Domain: Range:

b.

Domain: Range:





5. a. Complete the difference column for this table. b. Find a recursive function definition and an explicit (closed form) function definition that agree with the table below.

Input, n Output, p(n)

€

Δ

0 -8

1 -5

2 -2

3 1

4 4

Recursive definition:

€

p(n) =" # $

Explicit definition: p(n) =





6. For each function: a. Sketch a graph of the function below by making a table of values or using your graphing calculator. b. On the same graph, graph the inverse function or relation. Label both graphs to distinguish them. c. Is the inverse a function or merely a relation? d. Find the inverse function or relation.

f(x)=

€

x2

+ 3 g(x)=

€

8x − 4 h(x)=

€

0.5x 2 j(x)=

€

−3x

i. f(x)=

€

x2

+ 3

Graph f(x) and its inverse.

Is the inverse a function? Write the inverse using the correct name for it, in this case

€

f −1(x).

ii. g(x)=

€

8x − 4 Graph g(x) and its inverse.

Is the inverse a function? Write the inverse using the correct name for it.





iii. h(x)=

€

0.5x 2 Graph h(x) and its inverse.


iv. j(x)=

€

−3x Graph j(x) and its inverse.






7. a. Which of the following recursive functions best fits the table below?

Input, n Output,

a(n)

0 2

1 -1

2 -7

3 -19

4 -43

5

i.

€

a(n) =2 if n = 0

a(n −1) − 3 if n > 0# $ %

ii.

€

a(n) =2 if n = 0

2⋅ a(n −1) − 5 if n > 0$ % &

iii.

€

a(n) =2 if n = 0

a(n −1) + 2n − 5 if n > 0# $ %

iv.

€

a(n) =2 if n = 0

a(n −1) − 2n − 2 if n > 0# $ %

b. Fill in the value for a(5) in the table using the definition you chose. 8. Write an equation for a linear function with a slope of 4 and passing through the point (5, -2).




Name: Date:

Week 4 Assignment Guide

B-‐Block C-‐Block

Monday Do Now 11: Functions Pop Quiz In Class: Inverse Functions, Graphically and Algebraically. Homework: Pages 306-‐208 # 3, 4 (a-‐f) (use your calculator), 5, and 7. The following problems are reach problems: 3c, 3e, 4e, and 4f. All the rest are standard problems.

Do Now 11: Functions Pop Quiz

In Class: Inverse Functions, Graphically and Algebraically. Homework: Pages 306-‐208 # 3, 4 (a-‐f) (use your calculator), 5, and 7. The following problems are reach problems: 3c, 3e, 4e, and 4f. All the rest are standard problems.

Tuesday Do Now: DN 11.5 – Evaluating Functions In Class: Finding Zeros with Calculators, Evaluating Functions with Calculators, Begin Review if Time Homework: None

Thursday DN 12 – Inverses of Functions In Class: Test Review Homework: Finish Test Review

DN 12 – Inverses of Functions In Class: Test Review Homework: Finish Test Review

Friday In Class: Unit 1 Test Homework: None

In Class: Unit 1 Test Homework: None

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