   SEARCH HOME Math Central Quandaries & Queries  if P(4,-5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6). Hi Carl,

Let me look at different functions y = g(x) and y = 4g(x - 5). How do these graphs compare?

Suppose I want to find the value of the second function at x = 2. To do this I find the value of the first function at x = 2 - 5 = -3. that is I look at the value of the first function 5 units to the left of x = 2. Once I find the value of the first function at x = -3 I multiply this number by 4 to get the value of the second function at x = 2. So look at the points you just identified on the two graphs. If you are at the point on the first graph then the corresponding point on the second graph is 5 units to the right and its y-value is 4 times the y-value of the point on the first graph. So, for example if (2 -3) is on the first graph then the corresponding point on the second graph has x-coordinate 2 + 5 = 7 and y-coordinate 4 -3 = -12.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.