SOLUTION: What is the reflection of the graph of y=2^x across the y axis? Y=-2^x Y=.5(2^x) Y=(1/2)^x Y=5(2^x)

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Question 973265: What is the reflection of the graph of y=2^x across the y axis?
Y=-2^x
Y=.5(2^x)
Y=(1/2)^x
Y=5(2^x)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
i believe it will be y = (1/2)^x

it was derived as follows:

you know that 2^2 = 4

you want some value of b^(-2) to be also equal to 4

you start with b^(-2) = 4

take the log of both sides of the equation to get:

log(b^(-2)) = log(4)

since log(b^a) = a*log(b), that equation becomes:

-2*log(b) = log(4)

divide both sides of that equation by -2 to get:

log(b) = log(4)/(-2)

evaluate that equation to get:

log(b) = .6020599913/(-2) = -.3010299957

by the basic law of logarithms that says y = log(x) if and only if 10^y = x, you get:

log(b) = -.3010299957 if and only if 10^-.301029997 = b

solve for b to get b = .5 which is equal to 1/2.

you wound up with b^(-2) = 4 if and only if b = 1/2.

your solution is therefore that y = (1/2)^x.

here's the graph of y = 2^x and y = (1/2)^x

you can see that these two equations are reflections of each other about the y-axis.

this may have been the hard way to derive it.

usually you just replace x with -x and you should get the equivalent equation that's a reflection of the original equation about the y-axis.

start with y = 2^x

replace x with (-x) to get:

y = 2^(-x)

that's the same as y = 1 / 2^x

since 1 to any power is equal to 1, that equivalent to y = 1^x / 2^x which is the same as y = (1/2)^x.

the solution was derived in two different ways.

i think the second way was easier.