Question 607288: Graph the function f(x)= -x, X<3,
3x-4, x>= 3
a) fund the domain
b) locate any intercepts
c) graph the function
d) find the range
e) is f continuous on its domain?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! a) The function is defined in two different ways for x<3 and for  , but it is defined for all x, so the domain is all the real numbers.
b) For x<3, f(x)=-x is a straight line going through the origin, since f(0)=0, so you could say that the x-intercept and the y-intercept are (0,0).
In the other part of the function, for ,
 and  , so there are no intercepts (no x=0 and no y=0) in that part of the function.
c) 
d) f(x)>-3 on both parts of the function, but there is no upper limit. Maybe you would describe the range as (-3,infinity), or maybe you are expected to use a different notation.
e) No. The function is obviously discontinuous at x=3. While it is continuous at all other points of its domain, it is not continuous at all points of the domain.
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