Question

An exponential function in the form f(x) = ab�� + k is given. The linear function f(x) decreases through the ordered pairs (-2,6), (-1,4), (0,3), (1,2.5), (2,2.25), and (3,2.2125). What is the value of the vertical shift k?

1) one half
2) negative one half
3) 2
4) -2

Answer 1

The value of the vertical shift k in the exponential function is likely 2.2125, as the function described seems to be approaching this value as x increases.

Step-by-step explanation:

An exponential function in the form f(x) = abx + k has been presented. However, they describe a linear function that decreases through a set of ordered pairs. The question asks for the value of the vertical shift k in the given exponential function. To determine the value of k, we must look for the consistency in the y-values as x approaches infinity since the exponential growth or decay will dominate the linear term. Here, it seems there might be an error as no clear exponential pattern is provided, but the given values appear to approach a limit, suggesting k is the y-value the function is approaching. Based on the last few given y-values, we can infer that k is approximately 2.2125.