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

Answer 1

@Hero can you help me please

Answer 2

Actually, shifting a function of the form \(f(x) = 2^x + k\) h units to the right results in a function of the form \(f(x) = 2^{(x - h)} + k\)

Answer 3

So if you shifted \(f(x) = 2^x + 3\) ten units to the right, you'd end up with \(f(x) = 2^{x - 10} + 3\)

Shifting \(2^x + 3\) by k units would result in a vertical shift.

Answer 4

Here's the proof:
https://www.desmos.com/calculator/68iruncll3

Answer 5

@Glorenda49

Answer 6

I posted three functions on desmos.com:

\(f\left(x\right)=2^x+3\) (original function)
\(f\left(x\right)=2^{\left(x-10\right)}+3\) (shifted original function 10 units right)
\(f\left(x\right)=2^x-5\) (when k = -5, it shifts function 8 units down, not right)

I hope this makes sense.

Answer 7

I understand it

Answer 8

thanks :)

Answer 9

You're welcome