Question

Let f(x)=8(3)ˣ⁻² +2 .

The graph of f(x) is stretched vertically by a factor of 3 to form the graph of g(x) .

What is the equation of g(x)g(x) ?

g(x)=________

Answer 1

Vertical stretch would multiplying 8 by a number greater than 1. In this case, we have a factor of 3. 8 x 3 = 24.
Answer:
g(x) = 24(3)^(x-2) + 2

Answer 2

Answer:
`g(x) = 24(3)^(x-2)+2`

Explanation:

If an exponential function is represented by,

`f(x) = a e^b (x - c) + d`

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,

`f(x) = 8(3)^(x-2)+2`

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,

`g(x) = 24(3)^(x-2)+2`