Function of AS P1

[allysaleemally]

How do you find the range of a function and the domain of the inverse of that function in the form of a(x+b)^2 + c
or in the form of a-bcosx??
could please expain how to find the range and what do the values a,b,c denote?????

Thanks a million.

 

[donorsolutions]

Finding a range of a function when we get the function in the form a(x-b)^2 +c is pretty easy.
Just notice the coefficient of the term 'a' given in the above equation.
If its negative , the function has a maximum turning point
If its positive , the function has a minimum turning point.

Situation if Max Turning Point:
If turning point is maximum then all the values in the graph or the graph lies below the turning point, thats how the turning point becomes maximum.In such cases the range is f(x) is less than equal to +c.

Situation if Min Turning Point:
If turning point is minimum then all the values in the graph or the graph lies above the turning point, thats how the turning point becomes minimum.In such cases the range is f(x) is greater than equal to +c.

The Turning Point of The Graph is Given by, in the above equation (b,c)

Remember the following points:
Range of f(x) = Domain of f-1(x)
Domain of f(x) = Range of f-1(x)

Hope that helps and try doing the questions

 

[donorsolutions]

Another tip, that helps a lot and candidates often forget. When a line has equation in the form y=kx (where k can be any constant), the line passes through the origin and has no y intercept.