I'm going to assume that you can draw the graph of when x is positive. If that's part of what you're having trouble with, post again and I (or someone else) will help you with that.

It usually helps to consider what happens when x is positive and when x is negative separately. Or in the general case, look at what's inside the absolute value and figure out when it's positive and what happens then, then when it's negative and what happens then.

So in (d)(i), you're asked to graph . When x is positive, this is just . And when x is negative, the numerator, , is the same as when it's positive, while the denominator, x, changes sign. So the function has the opposite sign to the left of the y-axis.

In (d)(iii), when x is positive, the functions g and h are the same, since . And of course, g(x) is the same as in part (i), but for h(x), both the numerator and denominator are the same sign as when x is positive, so you have the same y-value for -x as you did for x. So you can see the graphs of g(x) and h(x) in the answers.

And since when x is negative, g(x) = -h(x), h(x) > g(x) whenever h(x) is positive, which you can also see in the graph.

- Hollywood