Question

The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 2 units, then what is the value of k?

Group of answer choices

k = 2

k equals one half

k = −2

k equals negative one half

Answer 1

The value of \( k \) that shifts \( f(x) = (0.5)^x \) down by 2 units is \( k = 2 \).

Certainly! The function
`\( f(x) = (0.5)^x \)`represents an exponential decay graph. The function
`\( g(x) = (0.5)^x - k \)` is obtained by shifting
`\( f(x) \)` down by 2 units.

To find the value of
`\( k \)` in this context, we know that the shift is downwards by 2 units. In exponential functions, shifting vertically means adjusting the constant term outside the function.

In
`\( f(x) = (0.5)^x \)`, there's no initial constant added or subtracted, so
`\( k \)` will be directly the value by which the function is shifted down, which is 2 in this case. Therefore,
`\( k = 2 \)`.

The function
`\( g(x) = (0.5)^x - 2 \)` represents the original function
`\( f(x) = (0.5)^x \)`shifted down by 2 units.

So, among the choices provided, the correct value for
`\( k \)` is indeed
`\( k = 2 \).` This signifies that the function
`\( g(x) \)` is the same as
`\( f(x) \)`shifted downwards by 2 units.