Question 739631
increasing: (-infinite, -1),decreasing: (3, infinite) and a constant: [-1,3] ?There is an infinite number of options.
Here is the graph of a continuous function that meets those requirements:
{{{drawing(300,300,-5,10,-10,5,
grid(0),
blue(line(-5,-8,-1,2)),
blue(line(-1,2,3,2)),
blue(line(3,2,10,-5))
)}}}
 
{{{f(x)=(matrix(2,3,-2x,if,x<-1,x+3,if,x>=-1))}}}
{{{g(x)=-2x}}} is a linear function with {{{g(-5)=10}}} and {{{g(-1)=2}}}
{{{f(x)=g(x)}}} for {{{x<-1}}} so I can draw that part of the graph for {{{f(x)}}} based on {{{g(x)}}}
{{{h(x)=x+3}}} is a linear function with {{{h(-1)=2}}} and {{{h(5)=8}}}
{{{f(x)=h(x)}}} for {{{x>=-1}}} so I can draw that part of the graph for {{{f(x)}}} based on {{{h(x)}}}
{{{drawing(300,300,-5,5,-2,13,
grid(1),
blue(line(-5,10,-1,2)),
blue(line(-1,2,6,9))
)}}}