Piecewise Function

When functions is determined by different formulas on different intervals then function is piecewise.

For example, `f(x)={(1-x if x<0),(x^2 if x>=0):}` is piecewise because on interval `(-oo,0)` `f(x)=1-x` and on interval `[0,oo)` `f(x)=x^2`. piecewise function

Now find `f(-2)`, `f(1)`, `f(0)` and draw graph of this function.

Remember that function is a rule. In this case it tells us that if `x<0` then apply `f(x)=1-x`, otherwise apply `f(x)=x^2`.

Since `-2<0` then we apply `f(x)=1-x`: `f(-2)=1-(-2)=3`.

Since `1>0` then we apply `f(x)=x^2`: `f(1)=1^2=1`.

Since `0>=0` then we apply `f(x)=x^2`: `f(0)=0^2=0`.

Now, to draw this function we draw graph of the function `f(x)=1-x` on interval `(-oo,0)` and graph of the function `f(x)=x^2` on interval `[0,oo)`.

Note, that open dot indicates that it doesn't belong to the graph. Indeed, `f(0)=0`, so point (0,0) is on the graph, but (0,1) is not.