Question

The function f(x)=5(2)^x was replaced with f(x)+k , resulting in the function graphed below.
What is the value of k?
FYI: it is not -2

Answer 1

In this problem, you have to find the y- intercept of $f(x)=5(2)^x$. I graphed mine into a graphing calculator. An algebraic way to find it is to input x=0 in the function. The y-intercept is 5.  You can see the y-intercept for the new one is -2. That means we shifted the graph down 7 units. (Vertical Shift down 7)  
k=-7

Answer 2

When x = 0 you get the y intercept y = 5
So the new fction goes from 5 to -2 , i.e. 7 units down, so k is -7