Domain and Range

*Domain-the interval of x values where the graph exists.
*Range-the interval of y values where the graph exists.
*Zeros x-int root-set=0 solve for x.
*To be a function the graph must pass the vertical line test.
*If given points the domain is the list of all x-values and the range is the list of all y-values in { }.

To find the Domain and Range:

1. polynomials: domain (-infinity, infinity) always

range (-infinity, infinity) odd always

2. square root: y=square root of x+/-number +/-a

domain: 1. set inside the root=0 and solve

2. set up intervals

3. plug in, if you get a negative x is the interval

4. write answers in interval notation-use [ by the number

range [a,infinity)

3. square root: y=square root of number - x^2 +/-a

domain: 1. set inside =0 solve

2. put answers in [-, ]

range: [0,square root of number] if a=0.

[0+a,square root of number+a] if a is positive

[0-a,square root of number-a] if a is negative

4. fraction: domain: 1. factor top and bottom

2. cancel if possible and mark the number cancelled

3. set bottom =0 and solve for x-values

4. write in interval notation stopping at number's found in 2 and 3

5. absolute value: domain: (-infinity,infinity)

range: [0+a,infinity) if opens up and a is positive

[0-a,infinity) if opens up and a is negative

(-infinity,0-a] if opens down and a is negative

(-infinity,0+a] if opens down and a is positive

Example 1:

Find the domain and range and tell whether each is a funtion.

f(x)=1/x

1. can't factor

2. can't cancel

3. x=0

Example 2:

Find the domain and range and tell whether each is a funtion.

g(t)= t+2/t^2+5t+6

1. t+2/(t+3)(t+2)

2. the (t+2)'s cancel x=-2

3. t+3=0 t=-3

4. (-infinity,-3) u (-3,-2) u (-2,infinity)