1.

Which of the following pairs of graphs intersect? (i)y = x^(2) -xandy = 1 (ii)y = x^(2) - 2x + 3 and y= sin x (iii)y = x^(2) - x+1 andy = x-4

Answer»

Solution :(i) ` y = x^(2) - x ANDY = 1" intersect if "x^(2) - x = 1or x^(2)-x-1 = 0`, which has real roots .
Hence, THEGRAPHS intersect.
(II) ` y = x^(2) - 2X+3 and y = sin x` intersect if ` x^(2) - 2x+3 = sin x or (x-1)^(2) + 2=sin x`, which is not possible SINCE L.H.S. has least value 2, while R.H.S. has maximum value 1.
`(iii) y = x^(2)-x + 1 and y = x - 4" intersect if " x^(2) - x+1 = x-4or x^(2) -2x + 5 = 0`, which has non-real roots. Hence, the graph do not intersect.


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