Can somebody thoroghly explain domain and range of a graph. Would the domain of this graph be (-infinity,3] because the vertex point is next to the 3?

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Question

Can somebody thoroghly explain domain and range of a graph. Would the domain of this graph be (-infinity,3] because the vertex point is next to the 3?

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aadi4502 · Answer

Before going to domain and range, we shall get to functions first. A function is a relation between an independent variable (x) and dependent variable (y) such that each value of x corresponds to a unique value of y. So, a domain shall be defined as all the permissible values (x) can take in order to give a unique value in (y). and range is defined as all the values of (y) taken by the equation when (x) is entered for various values in its domain.

Coming to your second question. No, the domain of the function will be from (-infinity to +infinity) because (X) can take all the values as shown in the graph. However it is a discontinuous graph. You need to define the graph as:
y=-1 x$$\epsilon(-\infty,3)$$
and y=-x+2 for all x belonging from 3 to +infty.
Reply if you have any firther doubts

agent0smith · Answer

@Aadi4502 the graph is not discontinuous, though.

aadi4502 · Answer

@agent0smith  yeah, sorry for the mistake. and thanks for correcting.