Robert N. answered • 05/23/19
University of FL Physics & Engineering Major w/ Strong Math Background
We'll start with the parent function y = 1/x. To stretch it in the y-direction by some factor, we should multiply y by that factor. So ystretched = 4y = 4/x. This works because for every x-value, the y-value, positive or negative, will now be four times further away from the x-axis. Then, to shift in the x-direction to the right by some amount, we should replace x in the equation with x - that amount. So yshifted(x) = y(x - 3) = 1/(x - 3). This is because for any value x1 that you plug into y(x) to get y(x1), plugging the value 3 units to the right of x1, or x1 + 3, into y(x - 3) gives y(x1 + 3 - 3) = y(x1). In other words, for the new graph you end up getting the same y-value at an x position 3 units more to the right from every point in the original graph. Note that shifting left is the same as shifting right by a negative value. This means that to shift left you do x + that amount instead of x - that amount. Doing both stretching and shifting here (in this case the order does not matter) yields yfinal = 4/(x - 3).
