a) The domain is the range of numbers for which the function is defined. For example has the domain because it is defined everywhere except where x is negative.

b) The x intercept occurs when f(x)=0, the y intercept occurs when x=0

c) consider what happens when x becomes very large.

d) f is increasing when the slope is positive

e) The maxima and minima occur when f'(x)=0

You are asked to find the VALUES of f(x) at these maxima and minima so determine the value of f(x) at the points

Suppose x=a satisfies f'(x)=0 so that f'(a)=0. The point is a maximum if f''(a)<0 and a minimum is f''(a)>0. If f''(a)=0 it is neither a maximum or minimum.

With the values from e) and knowing the asymptotes if they exist you can sketch f.