how do you sketch f(x) = ax+b? i know how to sketch when a and b are given numbers, but I'm not sure what to do now as a and b could be any numbers and so the graph could literally look like any line. thankz.
It could look like anything, but you should know that 'b' is the y-intercept and 'a' gives the direction of the line.
Therefore sketching y=ax+b for any 'a' and 'b', simply mark 'b' on the y-intercept and draw a line through it in the direction given by 'a'.
I'd break it up into a number of cases and sketch an example of each:
Case 1a: a > 0 and b > 0.
Case 1b: a > 0 and b = 0.
Case 1c: a > 0 and b < 0
Case 2a: a < 0 and b > 0.
Case 2b: a < 0 and b = 0.
Case 2c: a < 0 and b < 0.
Case 3a: a = 0 and $\displaystyle b \neq 0$.
Case 3b: a = 0 and b = 0.