Consider the following parental function f(x):
[tex]f(x)=0.5^x[/tex]Now, according to the problem, the graph of this function is replaced by the graph of g(x) which is defined as a follows:
[tex]g(x)=0.5^x\text{ - k}[/tex]Notice that the transformation that was applied to the function f(x) is a vertical shift of the graph. If k>0, by definition, the vertical shifts of the graphs are:
1) To graph y = f(x) + k, shift the graph of y=f(x) upward k units.
2) To graph y = f(x) - k, shift the graph of y=f(x) downward k units.
According to the second definition, if g(x) is obtained by shifting f(x) down by 3 units, the value of k would be 3 and we obtain:
[tex]g(x)=0.5^x\text{ - 3}[/tex]we can conclude that the correct answer is:
Answer:[tex]k\text{ = 3}[/tex]