SOLUTION: Graph the function y = |x+1|

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Question 180374: Graph the function y = |x+1|
Found 2 solutions by Mathtut, Electrified_Levi:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
plot points
:
say x=1 then y=abs(x+1) =abs(2)=2
(1,2)
:
say x=-3 then y=abs(x+1)=abs(-2)=2
:
(-3,2)
:
you can plot as many points as you think it takes to get a picture of what the graph will look like
:
hope that helps


graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cabs%28x%2B1%29%29

Answer by Electrified_Levi(103) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, Hope I can help,
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Graph the function y = |x+1|
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Absolute value is how far the number is on the number line. Absolute value makes any number inside them positive.
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+abs+%28+-9%29+=+9+
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+abs+%28+-20+%29+=+20+
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+abs+%28+3+%29+=+3+
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Knowing this principle
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+y+=+abs+%28+x+%2B+1+%29+
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We know that "y" will always be positive, since "y" equals an absolute value
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All absolute value graphs look like a "V", the very point that the two lines meet will always be where "y" equals "0" ( since "0" is neither positive or negative, it doesn't have absolute value ), the "V" goes out from this point
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Let us graph a few points
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+y+=+abs+%28+x+%2B+1+%29+
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First we replace "x" with any number
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We will replace "x" with (-1)
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+y+=+abs+%28+x+%2B+1+%29+ = +y+=+abs+%28+%28-1%29+%2B+1+%29+ = +y+=+abs+%28+0+%29+,
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+y+=+0+
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+x+=+-1+
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Points are given as (x,y)
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Our point is ( -1,0 )
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+drawing+%28+900%2C900%2C+-20%2C+20%2C-20%2C20%2C+circle+%28-1%2C0%2C0.1%29%2C+blue+%28circle+%28-1%2C0%2C0.2%29%29%2C+graph+%28+900%2C900%2C-20%2C20%2C-20%2C20%29%29+
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We need to find at least two more points to make the graph, we need a point with "x" as a positive number, and one with "x" as a negative number
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We will replace "x" with "5"
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+y+=+abs+%28+x+%2B+1+%29+ = +y+=+abs+%28+5+%2B+1+%29+ = +y+=+abs+%28+6+%29+
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+y+=+6+
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+x+=+5+
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Our point is (x,y), ( 5,6 )
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+drawing+%28+900%2C900%2C+-20%2C+20%2C-20%2C20%2C+circle+%28-1%2C0%2C0.1%29%2C+blue+%28circle+%28-1%2C0%2C0.2%29%29%2C+circle+%285%2C6%2C0.1%29%2C+blue+%28circle+%285%2C6%2C0.2%29%29%2C+graph+%28+900%2C900%2C-20%2C20%2C-20%2C20%29%29+
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We will now replace "x" with a negative number
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We will replace "x" with +-+12+
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+y+=+abs+%28+x+%2B+1+%29+ = +y+=+abs+%28+%28-12%29+%2B+1+%29+ = +y+=+abs+%28+-11+%29+
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+y+=+11+ ( since absolute value makes all negatives positive )
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+y+=+11+
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+x+=+-12+
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Our point is (x,y) , ( -12,11 )
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+drawing+%28+900%2C900%2C+-20%2C+20%2C-20%2C20%2C+circle+%28-1%2C0%2C0.1%29%2C+blue+%28circle+%28-1%2C0%2C0.2%29%29%2C+circle+%285%2C6%2C0.1%29%2C+blue+%28circle+%285%2C6%2C0.2%29%29%2C+circle+%28-12%2C11%2C0.1%29%2C+blue+%28circle+%28-12%2C11%2C0.2%29%29%2C+graph+%28+900%2C900%2C-20%2C20%2C-20%2C20%29%29+
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We could now draw the equation, by drawing a line from ( -1,0 ) to ( -12, 11 ) then keep drawing the line after ( -12 , 11 ), then we would draw a line from (-1,0) to (5,6) and beyond
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We could find more points if we wanted to,
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"x" as (-7), +y+=+abs+%28+x+%2B+1+%29+ = +y+=+abs+%28+%28-7%29+%2B+1+%29+ = +y+=+abs+%28+-6+%29+
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+y+=+6+ ( absolute value )
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+x+=+-7+
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Our point is ( -7,6 )
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+drawing+%28+900%2C900%2C+-20%2C+20%2C-20%2C20%2C+circle+%28-1%2C0%2C0.1%29%2C+blue+%28circle+%28-1%2C0%2C0.2%29%29%2C+circle+%285%2C6%2C0.1%29%2C+blue+%28circle+%285%2C6%2C0.2%29%29%2C+circle+%28-12%2C11%2C0.1%29%2C+blue+%28circle+%28-12%2C11%2C0.2%29%29%2C+circle+%28-7%2C6%2C0.1%29%2C+blue+%28circle+%28-7%2C6%2C0.2%29%29%2C+graph+%28+900%2C900%2C-20%2C20%2C-20%2C20%29%29+
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"x" as "10", +y+=+abs+%28+x+%2B+1+%29+ = +y+=+abs+%28+10+%2B+1+%29+ = +y+=+abs+%28+11+%29+
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+y+=+11+
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+x+=+10+
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Our point is (10,11)
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+drawing+%28+900%2C900%2C+-20%2C+20%2C-20%2C20%2C+circle+%28-1%2C0%2C0.1%29%2C+blue+%28circle+%28-1%2C0%2C0.2%29%29%2C+circle+%285%2C6%2C0.1%29%2C+blue+%28circle+%285%2C6%2C0.2%29%29%2C+circle+%28-12%2C11%2C0.1%29%2C+blue+%28circle+%28-12%2C11%2C0.2%29%29%2C+circle+%28-7%2C6%2C0.1%29%2C+blue+%28circle+%28-7%2C6%2C0.2%29%29%2C+circle+%2810%2C11%2C0.1%29%2C+blue+%28circle+%2810%2C11%2C0.2%29%29%2C+graph+%28+900%2C900%2C-20%2C20%2C-20%2C20%29%29+
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Here is the graph
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+drawing+%28+900%2C900%2C+-20%2C+20%2C-20%2C20%2C+circle+%28-1%2C0%2C0.1%29%2C+blue+%28circle+%28-1%2C0%2C0.2%29%29%2C+circle+%285%2C6%2C0.1%29%2C+blue+%28circle+%285%2C6%2C0.2%29%29%2C+circle+%28-12%2C11%2C0.1%29%2C+blue+%28circle+%28-12%2C11%2C0.2%29%29%2C+circle+%28-7%2C6%2C0.1%29%2C+blue+%28circle+%28-7%2C6%2C0.2%29%29%2C+circle+%2810%2C11%2C0.1%29%2C+blue+%28circle+%2810%2C11%2C0.2%29%29%2C+graph+%28+900%2C900%2C-20%2C20%2C-20%2C20%2C+abs+%28+x+%2B+1%29%29%29+
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(for some reason graph doesn't make a complete "V" for some reason, don't worry )
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Hope I helped, Levi