Question

How do you graph `f(x)=(x-2) / (x+2)`?

Answer 1

Just to run through some general points:

`f(x) = (x-2) / (x+2)`
What is f(x) when x = 0?
`(0-2)/(0+2) = -2/2 = -1`
Thus our first point on the graph is (0,-1).
What is x at 1?
`(1-2)/(1+2) = -1/3`
Thus our second point on the graph is (1, -1/3).
We continue in this manner until you have enough points on the graph.

Explanation:

One thing to note: when `x=-2`, we have `4/0` (we can't divide by zero!) so our graph will not reach x=-2. Thus we can see an asymptote in our graph at x=-2.

As we can see on the y axis, when x is positive it never reaches `f(x) = 1` (as we will always be dividing x by the larger number x+2). The opposite is true when x is negative, as the nominator x will always be larger than the denominator until x=0.

graph{(x-2)/(x+2) [-10, 10, -5, 5]}