Question 441009: describe the graph of each function
y=3/x+2
and
y=3x^2
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! describe the graph of each function
y=3/x+2
and
y=3x^2
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The first graph you see is the function y=1/x
As you can see, it is symmetric about the origin with points, (1,1) and (-1,-1)
If you multiply this function by 3 you get y=3/x.
The curve is still symmetric about the origin, but it is pushed further away from the origin, with points, (2,3/2) and (-2/-3/2). If you add 2 to the function, you get y=3/x+2, the final configuration. In this case the function is no longer symmetric about the origin. What it does is shift the entire curve 3 units up. The graph below shows what the final configuration looks like.
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y=x^2
This is a parabola of the form, y=(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
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Since h and k do not appear in the function, they must be (0,0), that is, the vertex of the parabola is at the origin as you can see from the graph above. The multiplier, 3, affects the steepness of the curve. The larger the multiplier the narrower the parabola becomes. The graph below of y=3x^2 shows this
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