1. Find the natural domain of the following functions. Explain your results.
2. Given the equation y= x2 - 6x +8, find the following:
(i) For what values of x is y = - 10?
(ii) For what values of x is y = ≥ 0 ?
(iii) Find the minimum value of y.
(iv) Find the maximum value of y.
3. (a)Sketch the graph of y = x-1/x by translating, reflecting, compressing and stretching the graph of y =1/x
(b) Find an expression for f o g, given that:
4. Find the equation of all lines passing through the point (6, -1) for which the product of their x- and y- intercepts is 3. Sketch these lines.
5. (a) Find the amplitude and period, and sketch at least two periods of the following function:
y = 1/2 cos(3x - Π)
(b) Express the following expression as a single logarithm:
2ln(x+1) + 1/3 ln(x - cosx)
6. Find the expression for: (i) ) sin(cos-1x ) and (ii) tan(cos-1x).
7. Solve the following equation for x:
8. Find the limit of the following:
9. Find :