Chapter 6.1, Problem 38E

To determine

To find: the value of k.

Answer to Problem 38E

  $k=3$

Explanation of Solution

Given:

The graph:

  

Concept used:

Vertical translation:

The graph of $g\left(x\right)=f\left(x\right)+k$ is a vertical translation of the graph of f.

The vertical shift is k units up if $k>0$ and k units down if $k<0$ .

Comparing the given graphs of $f\left(x\right)={0.25}^x$ and $g\left(x\right)={0.25}^x+k$ , it can be observed that the graph of g is a vertical translation 3 unit upwards of the graph of f.

Thus, by the above definition of vertical translation it can be said that $k=3$ .