The graph of f(x) = 2^x + 4 shifts six units to the right when it is replaced with the graph of f(x) = 2^x - k. What is the value of k?

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The graph of f(x) = 2^x + 4 shifts six units to the right when it is replaced with the graph of f(x) = 2^x - k. What is the value of k?

Mathematics
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2 4 6 10
@jim_thompson5910 do you think you could help?
the x+4 is all in the exponent?

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Other answers:

yep
so is x-k ?
yep
to shift f(x) 6 units to the left, we replace every x with x+6
ok
so it would be x+6+4?
Correct \[\Large f(x) = 2^{x+4}\] \[\Large f(x+6) = 2^{x+6+4}\]
simplify x+6+4 and compare it to x-k to figure out what k would be
so it'll be x+10
so k=10?
x+10 x-k k = ???
it might help to rewrite x+10 as x-(-10)
im confused
wait would it be 10-k?
\[\Large x + 10\\ \Large x - (-10)\\ \Large x - (\color{red}{-10})\\ \Large x - \color{red}{k} \] So k = -10
but there isnt a -10 as an answer
oh I went the wrong direction. It's to the right, so x gets replaced with x-6
so it would be x+2?
f(x) = 2^(x+4) f(x-6) = 2^(x-6+4) f(x-6) = 2^(x-2) so k = 2
x-2 actually
thank you
i got it right :D
thank you so much
np

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