##### Reference no: EM13470

1. Find the natural domain of the following functions. Explain your results.

2. Given the equation y= x^{2} - 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^{-1}x ) and (ii) tan(cos^{-1}x).

7. Solve the following equation for x:

8. Find the limit of the following:

9. Find :

10. Find