Answer:
Part 1) [tex]f(x)=5[/tex]
Part 2) [tex]f(x)=2x+2[/tex]
Part 3) [tex]f(x)=-3[/tex]
Step-by-step explanation:
Find the piece-wise defined function in each interval
step 1
For [tex]x<-2[/tex] ----> the number -2 is not included
[tex]f(x)=5[/tex]
step 2
For [tex]-2\leq x<3[/tex]
Find the equation of the line
Let
[tex]A(-2,-2),B(0,2)[/tex]
the slope is equal to
[tex]m=\frac{2+2}{0+2}=\frac{4}{2}=2[/tex]
with the slope m and the point B find the equation of the line
Remember that the equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=2[/tex]
[tex]b=2[/tex] -----> the point B is the y-intercept
substitute
[tex]f(x)=2x+2[/tex]
step 3
For [tex]x\geq3[/tex]
[tex]f(x)=-3[/tex]
therefore
1) For x<-2
The value of f(x) is
[tex]f(x)=5[/tex]
2) For -2< x <3
The value of f(x) is
[tex]f(x)=2x+2[/tex]
3) For x>3
The value of f(x) is
[tex]f(x)=-3[/tex]
