Help With Domain and Range (1 Viewer)

[nabzilla]

Can someone please explain how to find the domain and range of a function with some easy steps and examples?

 

[ninetypercent]

find out the values which x and y cannot be equal to and then exclude these values when you make your statement.

e.g. y = 1/x.

x cannot be equal to zero, since x = 0 will be undefined. so therefore, the domain is all real x values but x = 0

y cannot be equal to zero. If y = 0, then 0 = 1/x. 1= 0, which is false. so therefore, the range is all real y values but y = 0

 

[nabzilla]

so i would write my answer as
domain: x>o
and
range: y>0

 

[addikaye03]

so i would write my answer as
domain: x>o
and
range: y>0

Well think logically.

x: All real x (x E R) but x=/=0 (check the graph, all values of x have a corresponding y-value except 0)

y: All real y (y E R) but y=/=0

This is because as the graph tends toward infinity, both positively and negatively, it tends towards zero but never reaches it.

x:>0 would mean that it is is in the first or fourth quadrant and y>0 would mean first quadrant.
Hence if we were to restrict the function y=1/x to the first quadrant then that would be the correct domain and range

 

[Cazic]

A function sends one set of numbers to another set of numbers. We call these sets of numbers the domain and range respectively.

For example, the function f defined by the relation f(x) = x² sends some numbers (the x's) to some new numbers (the f(x)'s, or y's if you like). Which x's is this function defined for? That is, what is its domain? Well, I'm pretty sure we can square any real number, so the function is defined for all real numbers, or equivalently, the domain of f is all real numbers (often denoted by blackboard bold R). Where does f send these real numbers then? That is, what is f's range? Well, 0² = 0, 1² = 1, 2² = 4, (-1)² = 1, (-2)² = 4, and so on. It looks like f sends all the real numbers to the non-negative real numbers. That is, the range of f is all non-negative real numbers, or {x in R : x greater than or equal to 0}.

You can apply the same ideas to the 1/x example already given.

Good luck.

 

[nabzilla]

so if i had the question:
y= x^2-4

i would write my domain and range as:
Domain= all real values of x
Range= y is greater than or equal to -4

am i right?

 

[Drongoski]

so if i had the question:
y= x^2-4

i would write my domain and range as:
Domain= all real values of x
Range= y is greater than or equal to -4

am i right?

Almost.

Domain: all real values

Range: all real values >= -4

 

[nabzilla]

oh ok awesome! thanks guys! this has helped me extremely!

 

[stevenboh]

man this is gonna confuse me.
in physics, we say that the range is the x value or how far a projectile is shot horzontilly.

but in maths, the range is the y value and is a vertical measurement.

GRRRRRRRRRRRRRRRRRRRR