We need to graph the given piecewise function.
To graph any piecewise function we do that into parts
Let's graph upper part first which is
[tex]f(x)=x^2+2[/tex]
restriction for that is [tex]-5 \leq x < 3[/tex]
that means we are free to pick any number for x that is between -5 and 3, including 3.
So we will find few points by plugging random numbers between -5 and 3.
Let's use x=-5, we get:
[tex]f(-5)=(-5)^2+2=25+2=27[/tex]
so first point is (-5,27).
similarly we can find other points like (0,2), (2,6), (-1,3) etc.
Now we join those points by a curved line.
[tex]-5 \leq x[/tex] means we use a close circle at -5
x<3 means use open circle at 3
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Repeat same process for 2nd part f(x)=x-4
choose any number between 3 and 7 like x=3, 4 etc
so we get points (3,-1), (4,0) etc
Now graph them
So the final graph will look like:
