Question

Pre-Calculus exponential functions help?

Answer 1

make an x/y table to get points and plot

Answer 2

where did the 1/4 and 1/2 come from?

Answer 3

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

Answer 4

Oh okay

Answer 5

So what do I do with the points from the table then? Plot them?

Answer 6

yes

Answer 7

But that table was only for 2^x, right? I still need a table for 2^-x?

Answer 8

yes

Answer 9

do you know your transformations?

Answer 10

kind of

Answer 11

so what if g(x) = f(-x) what is g compared to f? in other words, g is what transformation of f?

Answer 12

reflection?

Answer 13

about what?

Answer 14

the y axis

Answer 15

very good!
so f(x) = 2^x and g(x) = 2^(-x) hint, hint, wink, wink...

if you know one and you understand transformations, you really know both

Answer 16

so after I graph 2^x, then I just reflect it about the y axis for the graph of 2^-x?

Answer 17

right?

Answer 18

So they're exponential functions because they increase or decrease exponentially?

Answer 19

yes but where is the variable x?

Answer 20

I don't understand what you mean

Answer 21

\(f\left(x\right) = y = 2^x\)

Answer 22

x is in the exponent

Answer 23

and that's what is changing

Answer 24

thus an "exponential" function

Answer 25

ohhh okay!

Answer 26

so what if we're given the graph and need to find the function? (I have an example)

Answer 27

http://www.purplemath.com/modules/expofcns.htm

exponential functions are also characterized by multiplying in a recursive relation...
\[f(x)=2^x=2\cdot 2^{x-1}=2\cdot f(x-1)\]
so if you have a graph, divide f(x)/f(x-1) to find the base

Answer 28

how do we know what f(x) is?

Answer 29

f(2) = 9, what is f(1)?

Answer 30

2?

Answer 31

that's what it looks like to me...

so f(2)/f(1) = base

Answer 32

so 9/2 is the base?

Answer 33

that's what i think

Answer 34

okay, then what's the exponent part?

Answer 35

whoa... wait

Answer 36

what?

Answer 37

f(1) = 2 <- this one is not correct
f(2) = 9

f(0) = 1

it's 2 tick marks but how much is each tick mark?

Answer 38

I thought it showed that each mark is 1...

Answer 39

if you ask me, f(1) = 3 look closely at the spacing of the vertical tick marks.

the first tick is about half of the subsequent ticks

Answer 40

there are 5 marks to 9... 1 + 2 + 2 + 2 + 2 = 9

Answer 41

besides (9/2)^1 = 9/2 \(\ne\) 2 and
(9/2)^2 = 81/4 \(\ne\) 9