# The Domain And Range Of A Function Algebra 2 With Trigonometry Homework

**Definition of the Domain of a Function** For a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly.

also Step by Step Calculator to Find Domain of a Function

**Definition of the Range of a Function** The range of f is the set of all values that the function takes when x takes values in the domain.

Also Step by Step Calculator to Find Range of a Function

**Example 1:**

**Solution to Example 1**- x can take any real number
**except 1**since x = 1 would make the denominator equal to zero and the division by zero is not allowed in mathematics. Hence the domain in interval notation is given by

(-infinity , 1) U (1 , +infinity)

__ Matched Problem 1:__ Find the domain of function f defined by

Answers to matched problems 1,2,3 and 4

__ Example 2:__ Find the domain of function f defined by

**Solution to Example 2**

- The expression defining function f contains a square root. The expression under the radical has to satisfy the condition

2x - 8 >= 0 for the function to takevalues.**real** - Solve the above linear inequality

x >= 4 - The domain, in interval notation, is given by

[4 , +infinity)

**Matched Problem 2:**

__ Example 3:__ Find the domain of function f defined by:

**Solution to Example 3**- The expression defining function f contains a square root. The expression under the radical has to satisfy the condition

-x >= 0 - Which is equivalent to

x <= 0 - The denominator must not be zero, hence x not equal to 3 and x not equal to -5.
- The domain of f is given by

(-infinity , -5) U ( -5 , 0]

__ Matched Problem 3:__ Find the domain of function f defined by:

__ Example 4:__ Find the range of function f defined by:

**Solution to Example 4**

- The domain of this function is the set of all real numbers. The range is the set of values that f(x) takes as x varies. If x is a real number, x
^{2}is either positive or zero. Hence we can write the following:

x^{ 2}>= 0 - Subtract -2 to both sides to obtain

x^{ 2}- 2>= -2 - The last inequality indicates that x
^{2}- 2 takes all values greater that or equal to -2. The range of f is given by

[ -2 , +infinity) - A graph of f also helps in interpreting the range of a function. Below is shown the graph of function f given above. Note the lowest point in the graph has a y (= f (x) ) value of -2.

Помнишь, что случилось в прошлом году, когда Стратмор занимался антисемитской террористической группой в Калифорнии? - напомнила. Бринкерхофф кивнул. Это было одним из крупнейших достижений Стратмора.

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