SOLUTION: Graph the piecewise continuous function f (x)= {x,-2<x<1 just below x,-2 is x^2+1,x_>1 the underline is actually the greater than or equal symbol with my keyboard

Algebra.Com
Question 287929: Graph the piecewise continuous function
f (x)= {x,-2 x^2+1,x_>1
the underline is actually the greater than or equal symbol with my keyboard i am unable to type in that syymbol. I am 100 percent stuck and confused on how to solve this problem I also have to graph it any help would be appreciated if there is confusion on how i typed it let me know I tried to copy and paste but wouldnt let me for some reason.
Eric

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!


First we draw the graph of 



But there is a restriction of , therefore
we must chop it off except where it is directly above
or below the part where x is beteen -2 and 1, like this:



Next we notice that the restriction is ,
so we place open circles at the ends since the graph
has no point directly below the part of the x-axis where 
 is on the x-axis or directly above the x-axis
where  is on the x-axis.  The graph does not 
include the point (-2,-2) or the point (1,1). The open 
circles indicate that the graph does not include that point. 
 


Next we draw the graph of 



But there is a restriction of , therefore
we must chop it off except where it is directly above
the part of the x-axis where x is greater than 1, like this:



Next we notice that the restriction is ,
so we place a closed circle at the end since the graph
has a point directly above where  is on the
x-axis, since the graph includes point (1,2).



That's the graph of 




Edwin

RELATED QUESTIONS

Graph the piecewise continuous function f(x)={x,-2=1 Sorry I... (answered by Fombitz)
Sketch the graph of the below piecewise function: f(x) = {5 , x>2} 2x-1 , (answered by Alan3354)
The formula for a piecewise-defined function is given below.... (answered by Edwin McCravy)
Given the following piecewise function for f(x), solve: 1/2x, x < 1 x^2, x = 1 ln(x), (answered by math_tutor2020)
GRAPH THE PIECEWISE FUNCTION GIVEN BY f(X)= { X+1 IF X < O (answered by Fombitz)
For the following piecewise defined function find f(-1) f(x)={x^2+1,......x<0... (answered by )
For the following piecewise defined function find f(1) f(x) = {x^2+1,....x<0... (answered by longjonsilver)
Represent the graph of the piecewise function y=f(x-1)-2 (answered by Fombitz)
Represent the graph of the piecewise function y=f(x-1)-2 (answered by Fombitz)