The function f(x) = {1/5}^x is translated up to 4 units. Which equation represents the translated function?

Solution:

Given, function f(x) = {1/5}^x

We have to translate the function upwards by 4 units.

For the base function f(x) and a constant k, the function is given by

g(x) = f(x) + k

The value of k determines the direction of shift.

If k > 0, the graph g(x) shifts k units upward and

If k < 0, the graph g(x) shifts k units downward.

To translate a function upward by 4 units we add a constant of 4 to the given function.

g(x) = f(x) + 4

g(x) = {1/5}^x + 4

Therefore, g(x) = {1/5}^x + 4.

The function f(x) = {1/5}^x is translated up to 4 units. Which equation represents the translated function?

Summary:

The function f(x) = {1/5}^x is translated up to 4 units. The equation representing the translated function is g(x) = {1/5}^x + 4.