Answer: [tex]g(x) = 24(3)^{x-2}+2[/tex]
Step-by-step explanation:
If an exponential function is represented by,
[tex]f(x) = a e^b (x - c) + d[/tex]
Where, the different type of modification in the graph occurs by changing the following values,
c - Translate Graph Horizontally
b - Horizontal Stretching ( scale factor > 1 ) or Compression (0 < scale factor < 1)
a - Vertical Stretching( scale factor > 1) or Compression (0 < scale factor < 1)
d - Translate Graph Vertically
Here, the given function is,
[tex]f(x) = 8(3)^{x-2}+2[/tex]
Thus, if the graph of f(x) is stretched vertically by a factor of 3 ( greater than 1 ) to form the graph of g(x).
Then, the value of 8 is increased 3 times.
Hence, the transformed function is,
[tex]g(x) = 24(3)^{x-2}+2[/tex]
