Answer:
Detailed explanation:
* Let’s clarify the procedure for solving this problem
- An exponential function can be expressed as , where
a signifies the starting amount (x = 0), and b denotes the growth factor
- If b > 1, it qualifies as an exponential growth function
- If 0 < b < 1, it is categorized as an exponential decay function
- Horizontal translation to the right by h units results in the new function being
- Conversely, if translated to the left by h units, the function modifies to
- A vertical upward shift by k units alters the function to
- A vertical downward shift by k units means the new function accounts for
* Now, let’s solve the problem
∵ f(x) is an exponential function
∵ The points (0, 1), (1, 10), (2, 100) are points of f(x)
- g(x) is the transformation of f(x)
∵ The points (3, 1), (4, 10), (5, 100) belong to g(x)
∵ The point (0, 1) on f(x) transforms to (3, 1) on g(x)
∵ The point (1, 10) on f(x) transforms to (4, 10) on g(x)
∵ The point (2, 100) on f(x) translates to (5, 100) on g(x)
∵ Notably, all y-coordinates of f(x) match those of g(x)
indicating no vertical translation
∴ Hence, no vertical translation occurred
∵ The x-coordinates of f(x) are increased by
3 units to yield the x-coordinates for g(x)
∴ This shows that f(x) is translated 3 units to the right
∵
∴
- Refer to the corresponding graph for greater clarity
# The red curve denotes f(x)
# The blue curve signifies g(x)
