Sumithra wrote:
Would appreciate if someone could shed some light on how to view an equation/inequality in xy-plane, for both straight lines and curves?
For lines, curves or any functions represented on an XY Plan, the concepts remain similar.
o y > f(x)
On the XY plan, the matching values of y are "above" the draw of y = f(x).
To know where is the concerned region, u can use 1 value of x : x=0 (if definied on 0), calculate f(0) and then look where is a value of y such that y > f(0). U will be "above" the f(x).
Ex 1 : For the line f(x) = 3*x+1, y > f(x) is in green (fig 1). f(0) = 1 so u know that the point (0,2) is in good region. Now, we can draw the region limited by the line and containing (0,2).
Ex 2 : For the line f(x) = -2*x-1, y > f(x) is in green (fig 2). f(0) = -1 so u know that the point (0,0) is in good region.
Ex 3 : For the line f(x) = x^2 -2*x -1, y > f(x) is in green (fig 3). f(0) = -1 so u know that the point (0,0) is in good region.
o y < f(x)
On the XY plan, the matching values of y are "under" the draw of y = f(x).
To know where is the concerned region, u can use 1 value of x : x=0 (if definied on 0), calculate f(0) and then look where is a value of y such that y < f(0). U will be "under" the f(x).
Ex 4 : For the line f(x) = -x+1, y < f(x) is in green (fig 4). f(0) = 1 so u know that the point (0,0) is in good region.
Ex 5 : For the line f(x) = 2*x^2 +4*x -1, y < f(x) is in green (fig 5). f(0) = -1 so u know that the point (0,-2) is in good region.
Attachments
Fig1_y_above_3x+1.gif [ 2.88 KiB | Viewed 12214 times ]
Fig2_y_above_-2x-1.gif [ 2.76 KiB | Viewed 12208 times ]
Fig3_Y_above_Xpow2-2X-1.gif [ 2.66 KiB | Viewed 12206 times ]
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