The graphs of f(x) = 10x and its translation, g(x), are shown. On a coordinate plane, 2 exponential functions are shown. f (x) a

The correct choice is option A if you prefer not to read through all of that ^

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)