How do I determine the domain and range in a peicewise function graph?

Answer 1

If you have a function in which x is the independent variable and y is
the dependent variable, the domain is the set of all the x numbers.
Normally, x can be any number, but if it is inside a radical sign, you
need to see whether there are values of x that will make y imaginary.
Those x numbers can't be in the domain. If x is in the denominator of
a fraction, any value of x that would make the denominator zero must
be eliminated. If you can solve the equation for x in terms of y, you
can use the same procedure to determine the range. Now, this is not a
complete answer, but it addresses the great majority of cases.

If you have a function that is determined by one expression for some
values of x, and then is determined by another expression for other
values of x, then that function is what we call "piecewise." For
example, y = x^2 for x < 3 and y = 2x + 1 for x > or = 3. On the curve
y = x^2, x can't equal 3, so the end of the curve, (3,9), is open.
But on the line y = 2x + 1, x can equal 3, so the end of the line,
(3,7), is closed.

to find the domain and range of the function whose graph has some jump discontinuities and also some endpoints that are not included obtain the domain by tracing the points on the graph and plot the x-coordinates of the points on a horizontal axis
In a similar way, obtain the range by tracing the points on the graph and plot the y-coordinates of the points on a vertical axis

Answer 2

If f(x)=y and if f is a continuous function, then the values of x are elements of the domain of x; and the values of y are elements of the range of y. However, if the function is discontinuous then the values of x and y are parts of the domain and range of x and y respectively. In a piecewise function you obtain the required values from the graph!

Answer 3

Graph

The domain are all values on the x axis

The range are all values on the y axis