Question

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?

Answer 1

2

4

6

10

Answer 2

@jim_thompson5910 do you think you could help?

Answer 3

the x+4 is all in the exponent?

Answer 4

yep

Answer 5

so is x-k ?

Answer 6

yep

Answer 7

to shift f(x) 6 units to the left, we replace every x with x+6

Answer 8

ok

Answer 9

so it would be x+6+4?

Answer 10

Correct

\[\Large f(x) = 2^{x+4}\]

\[\Large f(x+6) = 2^{x+6+4}\]

Answer 11

simplify x+6+4 and compare it to x-k to figure out what k would be

Answer 12

so it'll be x+10

Answer 13

so k=10?

Answer 14

x+10
x-k

k = ???

Answer 15

it might help to rewrite x+10 as x-(-10)

Answer 16

im confused

Answer 17

wait would it be 10-k?

Answer 18

\[\Large x + 10\\
\Large x - (-10)\\
\Large x - (\color{red}{-10})\\
\Large x - \color{red}{k}
\]

So k = -10

Answer 19

but there isnt a -10 as an answer

Answer 20

oh I went the wrong direction. It's to the right, so x gets replaced with x-6

Answer 21

so it would be x+2?

Answer 22

f(x) = 2^(x+4)

f(x-6) = 2^(x-6+4)

f(x-6) = 2^(x-2)

so k = 2

Answer 23

x-2 actually

Answer 24

thank you

Answer 25

i got it right :D

Answer 26

thank you so much

Answer 27

np