Question

1.Transform the graph of f(x) = 3^x to sketch g(x) = 3^-(x+1) -2. Show table of values and each transformation clearly.

2.Write two equations to represent the same exponential function with a y-intercept of 5 and an asymptote at y = 3. Investigate whether other exponential functions have the same properties. Use the transformations to explain your observations.

Thank you very much guys, I appreciate your help!

Answer 1

Given y = f(x),
(y-k) = f(x-h) is the same graph, shifted up k units and right h units.

Think of drawing a new set of axes at (h,k). Measuring from there, the new x values are reduced by h.

Now, you know what 3^x looks like.
3^-x is the same graph, flipped around the y-axis.

g(x)+2 = f(-(x+1))

is 3^x
(a) flipped over the y-axis
(b) shifted left by 1
(x) shifted down by 2