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What is Domain and Range?
The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:
- Domain = the set of all x-coordinates = {1, 2, 3, 4}
- Range = the set of all y-coordinates = {2, 3}
- Domain of any polynomial(linear, quadratic, cubic, etc) function is R.
- Domain of a square root function√x is x≥0.
- Domain of an exponential function is R.
- Domain of logarithmic function is x>0.
- To find the domain of a rational function y = f(x), set the denominator ≠ 0.
- Range of a linear function is R.
- Range of a quadratic function y = a(x-h)2+ k is:
y≥k, if a>0 and
y≤k, if a<0 - Range of a square root function is y≥0.
- Range of an exponential function is y>0.
- Range of logarithmic function is R.
- To find the range of a rational function y = f(x), solve it for x and set the denominator ≠ 0.
- Domain: The domain of the function is the set R.
- Range: The exponential function always results in positive real values.
- Domain: The domain of the functions is the set R.
- Range: The range of the functions is [-1, 1]
- Domain = R
- Range = [0, ∞)
- Domain:The domain of the function is the set R.
- Range:We already know that the absolute value function results in a non-negative value always. i.e., |6-x| ≥ 0, for all x.
- See whether the graph passes the vertical line test. Otherwise, it is not a function and we do not usually define domain and range for such curves.
- If there is any hole on the graph, then its coordinates shouldn't be in the domain and range.
- If there is a vertical asymptote, then the corresponding value of x shouldn't be there in the domain.
- If there is a horizontal asymptote, then the corresponding value of x shouldn't be there in the range.
- If the graph is broken into pieces, then we get multiple sets/intervals in the domain and range and we club all such sets/intervals by "union" symbol (∪).
- If there is an arrow at the end of a curve, then it means that the curve is supposed to be extended infinitely in that particular direction.
- All the x-values from -∞ to ∞ are covered by the graph (because of arrows, the two curves extend infinitely in the given directions). Hence, the domain = (-∞, ∞).
- All the y-values greater than or equal than or equal to 0 are covered by the graph (see there is no part of the curve that is below the y-axis). Hence, the range = [0, ∞).
- The domain and range of function is the set of all possible inputs and outputs of a function respectively.
- The domain and range of a function y = f(x) is given as domain= {x ,x∈R }, range= {f(x), x∈Domain}.
- The domain and range of any function can be found algebraically or graphically.
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