Suppose that the function g is defined, for all real numbers, as follows:?

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.

Draw an x -y coordinate system.

For g(x) = 3 if x < -1, the graph will be a horizontal line parallel to the to the x axis and in line with y = 3. This line will extend to -oo on the left side. Of course you can't draw it to minus infinity so the practice is to choose a suitable range of x values for your graph. Here -5 to 5 will do. The left hand side end of the line is just left as a line ending. The right hand end of the line will end in a small circle. The circle must be left empty to show that x = -1 is not included in the line.

For g(x) = 2 if x = -2 is just a point at x =1 y = 2. This point must be a small filled in circle which shows the point is included.

For g(x) = 1 the graph will be a horizontal line parallel to the x-axis and in line with y = 1. This line will extend to + oo on the right hand side but again just extend it to about x = 5 and leave the end just as the end of a line (no small circles.) The left hand end of the line will a small unfilled circle to show that x = -1 is not a point on this line.

That's is piecewise function which is defined by multiple sub-functions. The graph for this on is as follow:
at (-1 , 3) you have a circle and a horizontal line extending to the left i.e: -∞.
at (-1 , 2) you have a solid circle.
at (-1 , 1) you have a circle and a horizontal line extending to the right i.e: ∞.

I hope this helps.