Mth163
...Sketch a graph of the bacis expon. function y=2^x. it is stretched vertically by factor -2.5 then shifted -1.96 units vertically, what is the algebraic form of the function obtained?...I think that I might need to use y=Ab^x+c but I am not for sure...I think that I need to move the entire graph downward to -1.96 but I am not sure on that either...Thanks
You're definitely on the right track.
If you stretch the graph of y = f(x) by factor A, what you get is y = A f(x). Here you are stretching by factor -2.5 so you get y = -2.5 f(x), which for this function would be y = -2.5 * 2^x.
If you then shift the graph c units vertically, you just add c to your y values. You get y = A f(x) + c. Here you shift -1.96 units in the vertical direction so c = -1.96.
Your function therefore becomes y = -2.5 * 2^x - 1.96.