



 
Kapilan, I am going to illustrate with another function, g(x) = x^{2}  3. The technique is to plot h(x) = x^{2} and then look at how the graph changes when you subtract 3. h(x) = x^{2} is I graph I expect you know.
Subtracting 3 does not change the shape of the graph but it moves its position on the plane. For the function g(x) = x^{2}  3 when x = 0, g(x) = 3 and hence the graph passes trough (0, 3). Hence its graph is
What if you change the function h(x) = x^{2} by subtracting 3 from the input to the function, x, rather than the output h(x) to arrive at the function k(x) = (x  3)^{2}? Again you haven't changed the shape of the function, just where it sits in the plane. Here the vertex of the parabola is at x = 3 and hence the graph is shifted 3 units to the right and becomes
Harley  


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