D and R

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 { }.

The way to find Domain and range

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

range (-infinity, infinity) odd always


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


to find square root of 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


To find 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:


To find 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

Find domain and range


g(t)= t+2/t^2+5t+8


1. t+2/(t+4)(t+2)


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


3. t+4=0 t=-4


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