Question

The graph of a piecewise-defined function is shown below.

On the interval (x≤0, x≤1, x<1, x<0) the function is given by the rule (x= - 1, y= - 1, y=1, x=1), and on the interval (x≥0, x>1, x≥1, x>0) the function is given by the rule (y= - 1, x= - 1, y= 1, x= 1).

Answer 1

Note that the from $-\infty$ to 0, that is the left part, the function is the line y=1.

Similarly, from 0 (not included) to $\infty$, the function is y=-1.


Thus the function is given by the rule:

y=1, for x≤0,
y=-1, for x>0.


Remark: a horizontal line at height c, from the x-axis, is the graph of the function y=c.