Question 842971: Suppose that the function g is defined, for all real numbers, as follows:
g(x)=3, if x<-1
g(x)=2, if x=-1
g(x)=1, if x>-1
graph the function g. please help I don't know how to even start
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! your graph would look like this:
when x is less than -1, you have a line at y = 3 extending from minus infinity to -1 but not existing at x = -1.
that's the reason for the empty center dot at x = -1.
it says that the line extends to -1 but is not present at x = -1.
when x is equal to -1, you have a solid center dot at y = 2.
there is no line attached to y = 2 because y = 2 exists only at x = -1.
when x is greater than -1, you have a line at y = 1 extending from x = -1 to plus infinity.
the line does not exist at x = -1, therefore the point is represented by an empty center dot, not a solid center dot.
that solid line going all the way from the left of the graph to the right of the graph is the x-axis.
i forgot to label it as such.
don't confuse that with any of the other lines.
the vertical line in the middle is the y-axis.
the g represents the function name.
g(x) = 3 means that the value of y is always 3 regardless of what the value of x is. this function, however, is only active when x < -1.
g(x) = 2 means that the value of y is always 2 regardless of what the value of x is. this function, however, is only active when x = -1.
g(x) = 1 means that the value of y is always equal to 1 regardless of what the value of x is. this function, however, is only active when x > -1.
the domain of g(x) = 3 is all values of x < -1.
the range of g(x) = 3 is 3.
the domain of g(x) = 2 is x = -1 only.,
the range of g(x) = 2 is 2.
the domain of g(x) = 1 is all values of x > -1.
the range of g(x) = 1 is 1.
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