To determine the value of the vertical shift [tex]\(K\)[/tex] in the exponential function [tex]\(f(x) = a b^x + k\)[/tex], we need to identify the constant term in the function's form. This constant term represents the vertical shift [tex]\(K\)[/tex].
Given the options for the vertical shift [tex]\(K\)[/tex]:
1. [tex]\(3\)[/tex]
2. [tex]\(-3\)[/tex]
3. [tex]\(\frac{1}{3}\)[/tex]
We need to consider that the vertical shift [tex]\(K\)[/tex] can be either positive or negative, and any rational number constitutes a valid vertical shift.
Given these considerations, the possible values of [tex]\(K\)[/tex] are:
- [tex]\(3\)[/tex]
- [tex]\(-3\)[/tex]
- [tex]\(\frac{1}{3}\)[/tex] (which is approximately [tex]\(0.3333\)[/tex])
Thus, the values for the vertical shift [tex]\(K\)[/tex] in the exponential function [tex]\(f(x) = a b^x + k\)[/tex] could be:
1. [tex]\(3\)[/tex]
2. [tex]\(-3\)[/tex]
3. [tex]\(\frac{1}{3}\)[/tex]
These values represent the different possible vertical shifts for the given exponential form.
