The endpoint x = -2 is associated with the first and second sections of the domain. So, discontinuities could occur in the graph of the piecewise function at either, or both, of these points. In the given piecewise function, there are two shared endpoints of the domain sections: x = -2 and x = 2.

If both associated expressions evaluated at the endpoint are not equal, then the piecewise function does have a discontinuity at the point.

If both associated expressions evaluated at the endpoint are equal, then the piecewise function does not have a discontinuity at the point.

Then, evaluate each associated expression at the endpoint. To determine if a shared endpoint is a point of discontinuity in a piecewise function, determine the two sections of the domain that contain the endpoint. Solution:Дiscontinuities occur in piecewise functions at the shared endpoints of the domain sections. Example 3:ДЇind any discontinuities of the graph of the following piecewise function. Дiscontinuities of a function are points where the graph of a function has breaks or gaps. The x -intercept of the given piecewise function is (3, 0), and the y -intercept is (0, 4). In this case, x = 0 is in the second section of the function's domain.Д®valuate the expression that corresponds to the second section of the domain at x = 0. To find the y -intercept of the piecewise function, let x = 0.Дetermine the expression that corresponds to the section of the domain that contains x = 0. So, there is an an x -intercept at x = 3. Although, the solution x = 3 is in the third section of the domain. Even though x = 0 is a solution of the equation, it is not in third section of the domain. In this case, the equation yielded two solutions: x = 0 and x = 3. Set the third expression equal to zero, and solve.

Set the second expression equal to zero, and solve.Д®ven though the equation can be solved, x = 8 is not in second section of the domain therefore, there are no x -intercepts in the second section section of the domain. Since five cannot equal 0, there are no x -intercepts in the first section of the domain. Set the first expression equal to zero, and solve. After solving for x, make sure that the solution(s) of each equation exist in the corresponding domain. To solve the equation f(x) = 0, set each expression in the piecewise function equal to zero. To find the x -intercept, or zero, of the piecewise function, let f(x) = 0. Example 2:ДЇind the x - and y -intercepts of the following piecewise function. When the graph of a function touches or crosses the y -axis, x = 0. The y -intercepts of a function are the points where the graph of the function touches or crosses the y -axis. When the graph of a function touches or crosses the x -axis, f(x) = 0. The x -intercepts, or zeros, of a function are the points where the graph of the function touches or crosses the x -axis. Therefore, the domain of the function is. There is an open circle at x = 3, which indicates that the value is not in the domain of the function. There is a closed circle at x = -7, which indicates that the value is in the domain of the function. These discontinuities do not affect the domain of this function because the piecewise function is still defined at each discontinuity. It is seen that the graph has breaks, known as discontinuities, at x = -3 and x = 1. The given function is a piecewise function, and the domain of a piecewise function is the set of all possible x -values. What is the domain of the function graphed below? Solution: The range of a function is the set of all possible real output values, usually represented by y.

The domain of a function is the set of all possible real input values, usually represented by x. A piecewise function is a function defined by two or more expressions, where each expression is associated with a unique interval of the function's domain.

Piecewise function