Problems Which Are Due at the Beginning of Class: None

Pre-Class Problems13 for Tuesday, March 19

Problems which are due at the beginning of class: None

These are the type of problems that you will be working on in class. These problems will help with the problems inLesson 9. However, they are NOT from Lesson 9.

You can go to the solution for each problem by clicking on the problem letter.

Objective of the following problems: To find the domain and range of a function.

1.Find the domain and range of the following functions if the given points are on the graph of the function.

Objective of the following problems: To find the domain and range of the inverse function of a given function with the restricted domain if one is given.

2.Find the domain and range of the inverse function for the following functions if the given points are on the graph of the original function. If a restricted domain is given, then the given function will have an inverse function on that restricted domain.

c. for

cc. for

d. for

dd. for

g. for

gg. for

Objective of the following problems: To find the value of a function for a value in the domain of the function.

3.Find the following functional values.

a.is a set of points on the graph of the function f. Find , , and .

b. is a set of points on the graph of the function g. Find , , and .

c. is a set of points on the graph of the function h. Find , , and .

d. is a set of points on the graph of the function f. Find , , and .

e. is a set of points on the graph of the function g. Find , , and .

f. is a set of points on the graph of the function h. Find , , and .

g. is a set of points on the graph of the function f. Find , , and .

h.is a set of points on the graph of the cosine function. Find , , , , and.

i.is a set of points on the graph of the sine function. Find , , , and .

j.is a set of points on the graph of the tangent function. Find, , , and.

Objective of the following problems: To find the value of the inverse function for a value in the range of the function, which is the domain of the inverse function.

4.Find the following functional values.

a. is a set of points on the graph of the function f. Find , , and .

b. is a set of points on the graph of the function g. Find , , and .

c. is a set of points on the graph of the function h. Find , , and for .

cc. is a set of points on the graph of the function h. Find , , and for .

d. is a set of points on the graph of the function f. Find , , and for .

dd. is a set of points on the graph of the function f. Find , , and for .

e. is a set of points on the graph of the function g. Find , , and .

f. is a set of points on the graph of the function h. Find , , and .

g. is a set of points on the graph of the function f. Find , , and for .

gg. is a set of points on the graph of the function f. Find , , and for .

h. is a set of points on the graph of the cosine function. Find, , , and .

i. is a set of points on the graph of the sine function. Find , , , and .

j. is a set of points on the graph of the tangent function. Find , , , and .

Objective of the following problems: To find the inverse function for a given function.

5.Find the inverse function for the following functions.

a. b.

c. for d. for

e. for f. for

g. for

Solutions:

1a.

Domain =

Range =

NOTE: The given points are on the graph of the function . The actual domain of this function is the set of all real numbers and the actual range of this function is the set of all real numbers.

Back to Problem 1.

1b.

Domain =

Range =

NOTE: The given points are on the graph of the function . The actual domain of this function is the set of all real numbers and the actual range of this function is the set of all real numbers.

Back to Problem 1.

1c.

Domain =

Range =

NOTE: The given points are on the graph of the function . The actual domain of this function is the set of all real numbers and the actual range of this function is the closed interval .

Back to Problem 1.

1d.

Domain =

Range =

NOTE: The given points are on the graph of the function . The actual domain of this function is the set of all real numbers and the actual range of this function is the closed interval .

Back to Problem 1.

1e.

Domain =

Range =

NOTE: The given points are on the graph of the function . The actual domain of this function is the closed interval and the actual range of this function is the closed interval .

Back to Problem 1.

1f.

Domain =

Range =

NOTE: The given points are on the graph of the function . The actual domain of this function is the set and the actual range of this function is the set .

Back to Problem 1.

1g.

Domain =

Range =

NOTE: The given points are on the graph of the function . The actual domain of this function is the set and the actual range of this function is the open interval .

Back to Problem 1.

1h.

Domain =

Range =

NOTE: The given points are on the graph of the cosine function. The actual domain of this function is the set of all real numbers and the actual range of this function is the closed interval .

Back to Problem 1.

1i.

Domain =

Range =

NOTE: The given points are on the graph of the sine function. The actual domain of this function is the set of all real numbers and the actual range of this function is the closed interval .

Back to Problem 1.

1j.

Domain =

Range =

NOTE: The given points are on the graph of the tangent function. The actual domain of this function is the set and the actual range of this function is the set of all real numbers.

Back to Problem 1.

2a.

Domain =

Range =

NOTE: The given points are on the graph of the function . You will find the inverse function of this function in Problem 5a.

Back to Problem 2.

2b.

Domain =

Range =

NOTE: The given points are on the graph of the function . You will find the inverse function of this function in Problem 5b.

Back to Problem 2.

2c. for

Domain =

Range =

NOTE: The given points are on the graph of the function . You will find the inverse function of this function for in Problem 5c.

Back to Problem 2.

2cc. for

Domain =

Range =

NOTE: The given points are on the graph of the function . You will find the inverse function of this function for in Problem 5d.

Back to Problem 2.

2d. for

Domain =

Range =

NOTE: The given points are on the graph of the function .

Back to Problem 2.

2dd. for

Domain =

Range =

NOTE: The given points are on the graph of the function . You will find the inverse function of this function for in Problem 5e.

Back to Problem 2.

2e.

Domain =

Range =

NOTE: The given points are on the graph of the function .

Back to Problem 2.

2f.

Domain =

Range =

NOTE: The given points are on the graph of the function .

Back to Problem 2.

2g. for

Domain =

Range =

NOTE: The given points are on the graph of the function . You will find the inverse function of this function for in Problem 5f.

Back to Problem 2.

2gg. for

Domain =

Range =

NOTE: The given points are on the graph of the function . You will find the inverse function of this function for in Problem 5g.

Back to Problem 2.

2h.

Domain =

Range =

NOTE: The given points are on the graph of the cosine function. The domain of the inverse cosine function is the closed interval , which is the range of the cosine function, and the range of the inverse cosine function is the closed interval , which is the restriction put on the domain of the cosine function.

Back to Problem 2.

2i.

Domain =

Range =

NOTE: The given points are on the graph of the sine function. The domain of the inverse sine function is the closed interval , which is the range of the sine function, and the range of the inverse sine function is the closed interval , which is the restriction put on the domain of the sine function.

Back to Problem 2.

2j.

Domain =

Range =

NOTE: The given points are on the graph of the tangent function. The domain of the inverse sine function is the set of all real numbers, which is the range of the tangent function, and the range of the inverse tangent function is the open interval , which is the restriction put on the domain of the tangent function.

Back to Problem 2.

3a. is a set of points on the graph of the function f. Find , , and .

NOTE: The points on the graph of the function f are of the form.

:Answer: 2

:Answer: 11

:Answer:

NOTE: The given points are on the graph of the function .

Back to Problem 3.

3b. is a set of points on the graph of the function g. Find , , and .

NOTE: The points on the graph of the function g are of the form .

:Answer:

NOTE: The given points are on the graph of the function .

Back to Problem 3.

3c. is a set of points on the graph of the function h. Find , , and .

NOTE: The points on the graph of the function h are of the form .

:Answer: 16

:Answer: 1

:Answer: 4

NOTE: The given points are on the graph of the function .

Back to Problem 3.

3d. is a set of points on the graph of the function f. Find , , and .

NOTE: The points on the graph of the function f are of the form .

:Answer: 21

:Answer:

:Answer: 5

NOTE: The given points are on the graph of the function .

Back to Problem 3.

3e. is a set of points on the graph of the function g. Find , , and .

NOTE: The points on the graph of the function g are of the form .

:Answer:

:Answer: 2

NOTE: The given points are on the graph of the function .

Back to Problem 3.

3f. is a set of points on the graph of the function h. Find , , and .

NOTE: The points on the graph of the function h are of the form .

:Answer:

NOTE: The given points are on the graph of the function .

Back to Problem 3.

3g. is a set of points on the graph of the function f. Find , , and .

NOTE: The points on the graph of the function f are of the form .

:Answer:

:Answer: 1

NOTE: The given points are on the graph of the function .

Back to Problem 3.

3h. is a set of points on the graph of the cosine function. Find , , , , and .

NOTE: The points on the graph of the cosine function are of the form .

:Answer:

:Answer: 0

:Answer:

:Answer: 1

Back to Problem 3.

3i. is a set of points on the graph of the sine function. Find , , , and .

NOTE: The points on the graph of the sine function are of the form .

:Answer:

Back to Problem 3.

3j. is a set of points on the graph of the tangent function. Find , , , and .

NOTE: The points on the graph of the tangent function are of the form .

:Answer:

:Answer: 0

Back to Problem 3.

4a. is a set of points on the graph of the function f. Find , , and .

NOTE: The points on the graph of the function are of the form .

:Answer:

NOTE: The given points are on the graph of the function . In Problem 5a, it will be shown that .

Back to Problem 4.

4b. is a set of points on the graph of the function g. Find , , and .

NOTE: The points on the graph of the function are of the form .

:Answer:

NOTE: The given points are on the graph of the function . In Problem 5b, it will be shown that .

Back to Problem 4.

4c. is a set of points on the graph of the function h. Find , , and for .

NOTE: The points on the graph of the function are of the form , where .

:Answer: 2

:Answer: 1

:Answer: 3

NOTE: The given points are on the graph of the function . In Problem 5c, it will be shown that .

Back to Problem 4.

4cc. is a set of points on the graph of the function h. Find , , and for .

NOTE: The points on the graph of the function are of the form , where .

:Answer:

NOTE: The given points are on the graph of the function . In Problem 5d, it will be shown that .

Back to Problem 4.

4d. is a set of points on the graph of the function f. Find , , and for .

NOTE: The points on the graph of the function are of the form , where .

:Answer: 3

:Answer: 2

:Answer: 1

NOTE: The given points are on the graph of the function . It can be shown that .

Back to Problem 4.

4dd. is a set of points on the graph of the function f. Find , , and for .

NOTE: The points on the graph of the function are of the form , where .

:Answer:

NOTE: The given points are on the graph of the function . In Problem 5e, it will be shown that .

Back to Problem 4.

4e. is a set of points on the graph of the function g. Find , , and .

NOTE: The points on the graph of the function are of the form .

:Answer: 9

:Answer: 4

:Answer: 16

NOTE: The given points are on the graph of the function . It can be shown that .

Back to Problem 4.

4f. is a set of points on the graph of the function h. Find , , and .

NOTE: The points on the graph of the function are of the form .

:Answer: 2

:Answer:

:Answer: 4

NOTE: The given points are on the graph of the function . It can be shown that .

Back to Problem 4.

4g. is a set of points on the graph of the function f. Find , , and for .

NOTE: The points on the graph of the function are of the form , where .

:Answer: 4

:Answer: 2

:Answer: 1

NOTE: The given points are on the graph of the function . In Problem 5f, it will be shown that .

Back to Problem 4.

4gg. is a set of points on the graph of the function f. Find , , and for .

NOTE: The points on the graph of the function are of the form , where .

:Answer:

NOTE: The given points are on the graph of the function . In Problem 5g, it will be shown that .

Back to Problem 4.

4h. is a set of points on the graph of the cosine function. Find , , , and .

NOTE: The points on the graph of the cosine function are of the form .

:Answer:

Back to Problem 4.

4i. is a set of points on the graph of the sine function. Find , , , and .

NOTE: The points on the graph of the sine function are of the form .

:Answer:

Back to Problem 4.

4j. is a set of points on the graph of the tangent function. Find , , , and .

NOTE: The points on the graph of the tangent function are of the form .

:Answer:

:Answer: 0

Back to Problem 4.

5a. Back to Problem 5.

Set :

Solve for x:

Answer:

5b. Back to Problem 5.

Set :

Solve for x:

Answer:

5c. for Back to Problem 5.

Set :

Solve for x:

Since , then

Answer:

5d. for Back to Problem 5.

Set :

Solve for x:

Since , then

Answer:

5e. for Back to Problem 5.

Set :

Solve for x:

Since , then

Answer:

5f. for Back to Problem 5.

Set :

Solve for x:

Since , then

Answer:

5g. for Back to Problem 5.

Set :

Solve for x:

Since , then

Answer: