Best approach to plot functions?

Question

I know the graphs for functions such as: 1/x, 1/x^2, ln x, x^2, etc. However, what's the best approach to plot complex functions such as this: (1 + 3x), (2 - x^-2), (1 + 2x^3)? The reason is my instructor will ask us to find the area under the curve of such functions, but I only know the basic I mentioned above.

Answer 1

I'll take your examples, maybe you get an idea from that.
1) y = 1 + 3x
This is simply a straight line (single degree linear equation). y is always 1 greater than 3 times the x at that point. So it shouldn't be a problem to plot.

Lets take 3 first
3) y = 1 + 2x^3
lets cut it down to the simplest form: y = x^3. You can plot that, roughly. Similar to y=x^2, just more rapidly curving upwards, which, unless drawn to scale, hardly matters. Now try y = 2x^3. Just a constant factor of 2 is multiplied, again the curve rises upwards, without changing it's nature, though. Then add 1. So just shift your curve to accomodate the extra constant. For simplicity, you can try y-1 = 2x^3. It'll be the same.

2) y = 2 - x^-2
y - 2 = -x^-2
Use the same technique as above now. You know y=x^-2. Just negate it, you get y = -x^-2. Then adjust the curve to accomodate the -2. Ok?

Answer 2

When approaching a new function I found it best to plug and chug and plot. Start with inserting 0 for x and find the answer and then plot it on a graph. Then try 1, -1 and go out from there. Patterns usually emerge. Other easy numbers to work out are 2, 5, 10, and so on. Don't forget the negatives! You might play with the ones you mentioned at home. The more functions you see plotted, the easier it will be.

Answer 3

are you doing calculus yet? the best way is to take the first derivative and from that you can spot the slope at y=0 intercepts and the x values where the slope is 0 (line is flat).