Graphing Greatest Piecewise Function

[nycmathguy]

Section 1.6
Example 3

See attachment.

How do I graph a piecewise function by hand?

 

[MathLover1]

you are given f(x)={2x+3, x<=1
{-x+4, x>1

both parts are lines
first graph a line f(x)=2x+3, choose two values for x, find two points and draw a line through
it looks like this
see attached: graph 2x+3


but, since given x<=1, you actually draw a line up to point with x coordinate is x=1
f(x)=2*1+3=5
so, the point is (1,5)

do same with second part f(x)= -x+4, x>1 , draw a line starting from the point with x coordinate is x=1 (it’s a point (1,3) ) but exclude that point (that is a hole) and graph will look like this
see attached: graph -x+4


final graph will look like this

see attached: graph gr

 

[nycmathguy]

you are given f(x)={2x+3, x<=1
{-x+4, x>1

both parts are lines
first graph a line f(x)=2x+3, choose two values for x, find two points and draw a line through
it looks like this
see attached: graph 2x+3


but, since given x<=1, you actually draw a line up to point with x coordinate is x=1
f(x)=2*1+3=5
so, the point is (1,5)

do same with second part f(x)= -x+4, x>1 , draw a line starting from the point with x coordinate is x=1 (it’s a point (1,3) ) but exclude that point (that is a hole) and graph will look like this
see attached: graph -x+4


final graph will look like this

see attached: graph gr

Great study notes. Thanks. In addition to your reply, I will You Tube video clips when time allows. I can't to get off this insane OT schedule. August 6 cannot get here fast enough!