Question

okay so with exponential functions and looking at g(x)=2^x when its negative where does the 1/2 come from

Answer 1

can you rephrase your question; I don't understand

Answer 2

Do you mean the slope?

Answer 3

g(x)=2^x
the base of 2 is a fixed number and the x is your variable.
Let's look more closely at the function g(x) = 2x. To evaluate this function, we operate as usual, picking values of x, plugging them in, and simplifying for the answers. But to evaluate 2x, we need to remember how exponents work. In particular, we need to remember that negative exponents mean "put the base on the other side of the fraction line". this is what the notes gave me

Answer 4

i think i understand the question

Answer 5

you mean when x is negative.

Answer 6

yes!

Answer 7

So, a^-n = 1/a^n, for example.

Answer 8

you lost me

Answer 9

so don't forget that
\[b^{-n}=\frac{1}{b^n}\] so for example if you have
\[2^x\] hten
\[2^{-1}=\frac{1}{2}\] and
\[2^{-2}=\frac{1}{2^2}=\frac{1}{4}\]

Answer 10

thats right but that doesnt make sense on why the 1 is in the front and the variable is positive

Answer 11

a negative number in the exponent does not make the number negative

Answer 12

think of powers of ten

Answer 13

so your saying that when the exponet is negative you have to take the recipocal of it?

Answer 14

\[2^x = 1/(2^-n)\]

Answer 15

\[10^3=1000\]
\[10^2=100\]
\[10^1=10\]
\[10^0=1\]
\[10^{-1}=0.1\]
\[10^{-2}=0.01\]
\[10^{-3}=0.001\] etc

Answer 16

Wait, sorry!
\[2^x = 1/(2^-x)\]

Answer 17

yes the negative exponent means take the reciprocal

Answer 18

@razzles 2^{-n}

Answer 19

math is weird but not that weird. if you want the number to be negative, stick a minus sign in front

Answer 20

\[2^{-2}=\frac{1}{4}\]
\[-2^{-2}=-\frac{1}{4}\]

Answer 21

Law of exponents: \[x ^{-a} = 1/ x ^{a}\]

Answer 22

so with the negative numbers you move the decimal one place to the left?

Answer 23

how are you getting 1/4 from 2^-2

Answer 24

yes im this slow...

Answer 25

got it now :D thanks guys