Types of discontinuous functions, finding the domain and range of the discontinuous functions.
Domain and Range of Discontinuous Functions
Description: This lesson helps you how to find domain and range of discontinuous function.
Domain is the set of all real values that the independent variable "x" can assume. The domain of the function is set of all possible input values.
1) In the linear function y = x + 2, "x" can assume any real value.
2) In the square root function, y = √(x - 4). Here "x - 4 " has to be positive since square roots of negative numbers are not defined.
So the domain is x ≥ 4.
Range is the set of all real values that the dependent variable "y" takes. The range of a function refers to the output of a function.
1) In the linear function y = x + 2 there is no restriction on the values "y" takes. So the range of the function is set of all real values.
2) In the square root function, y = √(x - 4), y takes on only positive values (positive square root) and zero.
So the range is y ≥ 0.
Discontinuous functions are functions that ...
Function, domain, range, discontinuous functions, types of functions are discussed. The types of discontinuous functions are used to find the domain and range of the discontinuous functions.
Rate of Change and Function Domain & Range
Along with incomes, people's charitable contributions have steadily increased over the past
few years. The table below shows the average deduction for charitable contributions
reported on individual income tax returns for the period 2007 to 2012. Find the average rate
of change between 2009 and 2011.
Year Charitable Contributions
2. Given the following piecewise function:
(x) = -x +1 for x < 0
-1 for 0 ≤ x ≤ 3
-2x for x > 3
a. Find the domain.
b. Find the range.
c. Find the intercepts.
d. Is f continuous on its domain? If not, state where f is discontinuous.
e. Graph the function.