SOLUTION: GRAPH THE PIECEWISE FUNCTION GIVEN BY f(X)= { X+1 IF X < O { -X2 + 2 IF X >_ O X IS SQUARED AND THE SYMBOL IS GREATER THAN OR

Algebra ->  Algebra  -> Finance -> SOLUTION: GRAPH THE PIECEWISE FUNCTION GIVEN BY f(X)= { X+1 IF X < O { -X2 + 2 IF X >_ O X IS SQUARED AND THE SYMBOL IS GREATER THAN OR       Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 149323: GRAPH THE PIECEWISE FUNCTION GIVEN BY f(X)= { X+1 IF X < O
{ -X2 + 2 IF X >_ O


X IS SQUARED AND THE SYMBOL IS GREATER THAN OR = TO

Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
OK, let's pick the domain to go from -5 to 5.
From x=-5 to x=0 (not including x=0), the function is
f%5B1%5D%28x%29=x%2B1
From x=0 (including x=0) to x=5, the function is
f%5B2%5D%28x%29=-x%5E2%2Bx
Since for a straight line, we only need two points we will use x=-5,0 for f%5B1%5D.
f%5B1%5D%28-5%29=-5%2B1=-4
f%5B1%5D%280%29=0%2B1=1
Plot those two points, (-5,-4) and (0,1) and draw the straight line connecting them.
drawing%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2Cgrid%28+1+%29%2Ccircle%28+-5%2C+-4%2C+.1+%29%2Ccircle%280%2C1%2C.1%29%2Cgreen%28line%28+-5%2C+-4%2C+0%2C1%29%29%29
Next for the quadratic, we need more that 2 points, we'll pick x=0,1,2,3,4,5.
f%5B2%5D%280%29=-%280%29%5E2%2B2=2
f%5B2%5D%281%29=-%281%29%5E2%2B2=1
f%5B2%5D%282%29=-%282%29%5E2%2B2=-2
f%5B2%5D%283%29=-%283%29%5E2%2B2=-7
f%5B2%5D%284%29=-%284%29%5E2%2B2=-14
f%5B2%5D%285%29=-%285%29%5E2%2B2=-23
Plot those and connect those points.
Note the change in scale of the graph.
drawing%28+300%2C+300%2C+-5%2C+5%2C+-25%2C+5%2Cgrid%28+1+%29%2C%0D%0Acircle%280%2C2%2C.1%29%2C%0D%0Acircle%281%2C1%2C.1%29%2C%0D%0Acircle%282%2C-2%2C.1%29%2C%0D%0Acircle%283%2C-7%2C.1%29%2C%0D%0Acircle%284%2C-14%2C.1%29%2C%0D%0Acircle%285%2C-23%2C.1%29%2C%0D%0Ablue%28line%280%2C2%2C1%2C1%29%29%2C%0D%0Ablue%28line%281%2C1%2C2%2C-2%29%29%2C%0D%0Ablue%28line%282%2C-2%2C3%2C-7%29%29%2C%0D%0Ablue%28line%283%2C-7%2C4%2C-14%29%29%2C%0D%0Ablue%28line%284%2C-14%2C5%2C-23%29%29%2C%0D%0Acircle%28+-5%2C+-4%2C+.1+%29%2Ccircle%280%2C1%2C.1%29%2Cgreen%28line%28+-5%2C+-4%2C+0%2C1%29%29%29
Also, note the discontinuity at x=0.