1. Date
Functions Part Two and Arithmetic Combinations of Functions
Page #
Learning Targets—
I can identify the implicit and explicit form of a function.
I can find the domain of a function.
I can perform arithmetic combinations on functions.

2. Functions Part Two and Arithmetic Combinations of Functions
Admit Slip—
Page 69, #

3. Implicit and Explicit Form of a Function
In general, when a function f is defined by an equation in x and y, we say that the function f is given implicitly. If it is possible to solve the equation for y in terms of x, when we write y = f(x) and say that the function is given explicitly.
Implicit Form Explicit Form
3 x + y = 5 y = f(x) = -3x + 5
x2 – y = 6 y = f(x) = x2 – 6
xy = 4 y = f(x) = 4/x

4. Important Facts About Functions
For each x in a domain of a function f, there is exactly one image f(x) in the range; however, an element in the range can result from more than one x in the domain.
f is the symbol that we use to denote the function. It is symbolic of the equation that we use to get from an x in the domain to f(x) in the range.
If y = f(x), then x is called the independent variable or argument of f, and y is called the dependent variable or the value of f at x.

5. Finding the Domain of a Function
Often the domain of a function f is not specified; instead, only the equation defining the function is given. In such cases, we agree that the domain of f is the largest set of real numbers for which the value of f(x) is a real number. The domain of a function f is the same as the domain of a variable x in the expression f(x).

6. The implied domain of a function is the set
of all real numbers for which the expression
is defined.
In general, the domain of a function
excludes:
values that would cause division by zero
values that would result in the even root of a negative number.

7. Find the domain of each of the following functions:
a) f(x) = x2 + 5x b) c)

8. 1. Find the domain of each function.

9. 2. Find the domain of each function.

10. 3. Find the domain of each function.

11. 4. Find the domain of each function.

12. Domain
When we use function in applications, the domain may be restricted by physical or geometric considerations.
For example, the domain of the function f defined by f(x) = x2 is the set of all real numbers. However, if f is used to obtain the area of a square when the length x of a side is known, then we must restrict the domain of f to the positive real numbers, since the length of a side can never be 0 or negative.

13. Domain
Express the area of a circle as a function of the radius. Find the domain.
5. Express the area A of a rectangle as a function of the length x if the length of the rectangle is twice the width. Find the domain.

14. Domain
6. Express the gross salary G of a person who earns $10 per hour as a function of the number x of hours worked. Find the domain.

15. Arithmetic Combinations
Sum
Difference
Product
Quotient

16. Arithmetic Combinations
Find the following:

17. Arithmetic Combinations
7. Find the following:

18. Arithmetic Combinations

19. Arithmetic Combinations
8. Find the following:

20. Arithmetic Combinations

21. Arithmetic Combinations

22. Arithmetic Combinations

23. Arithmetic Combinations

24. Arithmetic Combinations
9. Find the following:

25. Functions Part Two and Arithmetic Combinations of Functions
Assignment—
Page (Are you prepared, Concepts and Vocabulary)
Page even (Find the domain)
Page , 64, 68, 70 (Use the arithmetic combinations)
Page , 96, (Applications)

26. Functions Part Two and Arithmetic Combinations of Functions
Exit Slip—
Page 70 #104