The graph of f(x) =2^(x+3) shifts 10 units to the right when it is replaced with the graph of f(x) = 2^(x-k). What is the value of k? 3 7 10 13

Question

The graph of f(x) =
`2^(x+3)` shifts 10 units to the right when it is replaced with the graph of f(x) =
`2^(x-k)`. What is the value of k? 3 7 10 13

Answer 1

7

Explanation:

Whenever you shifting an exponential function to the left/right, you're going to generally have the equation:
`y=2^(x-k)` where k is the shift. So in this case we can think of x+3 as x and k as 10, since the shift is 10. This gives you the equation: (x+3) - 10, which simplifies to x-7, meaning the k value in this case is going go be 7. You can also think of it as already being shifted 3 units to the left, and you shift it 10 units to the right, that means this new function will be shifted 7 units to the right relative to the origin. This means the k=7.