How do you graph the functions y equals 3x and y equals log x on the same set of axes Include domain range and asymptote for each?

Answer 1

[ y = 3x ] has no asymptote. Its range and domain are both infinite. Its graph is a

straight line, with a slope of 3, that enters from the bottom left, passes through the

origin, and exits at the top right. No matter how wide or high you make your

coordinate space, the graph still does that. You'll never find its end.

[ y = log(x) ] exists only in the right half of the plane, where 'x' is positive, so the

domain is from x=0 to infinite. Within that domain, 'y' ranges from negative infinite

to positive infinite.

The graph crosses the x-axis at [x=1].

To the left of that point, it plunges through all negative values, from zero to negative

infinite. The y-axis is the asymptote. That part of the graph looks like an inverted

hockey stick, with an infinite handle and a tiny tiny blade.

To the right of that point, where 'x' is greater than '1', the graph rises at a

slowly-increasing rate. It obviously curves upward, and one might think that

if we looked far enough out to the right, there might be another vertical

asymptote somewhere way out there in the land of great x-values. But

there isn't, and there are no x-values that it can't reach. The graph looks like

a right-side-up hockey stick with a monstrous blade and a timid handle.