1. ## functions...test tomorrow =/

Sketch a graph of an odd function that passes through the points (3,-1), (2,-2), and (-1,-1)

Can anyone explain how to do this? and for even functions as well..

Our teacher told us to use butcher paper to trace it but I still don't get it....

2. Originally Posted by realintegerz
Sketch a graph of an odd function that passes through the points (3,-1), (2,-2), and (-1,-1)

Can anyone explain how to do this? and for even functions as well..

Our teacher told us to use butcher paper to trace it but I still don't get it....
sketch a random function that passes through the points (not too random, something you can reproduce easily in various transformations), make sure that it has the following properties:

(a) to make the function odd, make sure that you can get the negative side (the part where the x-values are on the left side of the y-axis) by reflecting the positive side in the y-axis and then in the x-axis.

(b) to make the function even, make sure you can get the negative side by simply reflecting the positive side in the y-axis

remark: i hope you know what this really means in terms of points.

a function f(x) is odd if f(-x) = -f(x), so, for instance, if (3,-1), (2,-2), and (-1,-1) are on your graph, then (-3,1), (-2,2) and (1,1) must be also

a function f(x) is even if f(-x) = f(x). so, for instance, if (3,-1), (2,-2), and (-1,-1) are on your graph, then (-3,-1), (-2,-2), and (1,-1) must be also