Lipschitz Continuity

Question

Is this following graph Lipschitz continuous ?

$$ f(x) = 2x, -10<x<0;$$ $$=-3x^2, 0 \leq x \leq 1$$ $$=2x-5, 1 < x <10 $$

One can Put the following command in Matlab to plot the graph :

x=-10:0.0001:0;
y=2*x;
plot(x,y,'-')
hold all
x=0:0.0001:1;
y=-3*x.^2;
plot(x,y,'-')
x=1:0.0001:10;
y=2*x-5;
plot(x,y,'-')

Answer 1

$f$ is $C^1$ on $[0,1]$, hence Lipschitz continuous on this interval.

$f$ is also Lipschitz continuous on the other two intervals.

Lastly, $f$ is also continuous on $\mathbb R$. Hence $f$ is Lipschitz continuous on $\mathbb R $.