anonymous
  • anonymous
Pre-Calculus exponential functions help?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
make an x/y table to get points and plot
anonymous
  • anonymous
|dw:1443201477463:dw|

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anonymous
  • anonymous
where did the 1/4 and 1/2 come from?
anonymous
  • anonymous
\[2^{-1} = \frac{ 1 }{ 2^1 }=\frac{ 1 }{ 2 }\]\[2^{-2}=\frac{ 1 }{ 2^2 }=\frac{ 1 }{ 4 }\]
anonymous
  • anonymous
Oh okay
anonymous
  • anonymous
So what do I do with the points from the table then? Plot them?
anonymous
  • anonymous
yes
anonymous
  • anonymous
But that table was only for 2^x, right? I still need a table for 2^-x?
anonymous
  • anonymous
yes
anonymous
  • anonymous
do you know your transformations?
anonymous
  • anonymous
kind of
anonymous
  • anonymous
so what if g(x) = f(-x) what is g compared to f? in other words, g is what transformation of f?
anonymous
  • anonymous
reflection?
anonymous
  • anonymous
about what?
anonymous
  • anonymous
the y axis
anonymous
  • anonymous
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
anonymous
  • anonymous
so after I graph 2^x, then I just reflect it about the y axis for the graph of 2^-x?
anonymous
  • anonymous
right?
anonymous
  • anonymous
So they're exponential functions because they increase or decrease exponentially?
anonymous
  • anonymous
yes but where is the variable x?
anonymous
  • anonymous
I don't understand what you mean
anonymous
  • anonymous
\(f\left(x\right) = y = 2^x\)
anonymous
  • anonymous
x is in the exponent
anonymous
  • anonymous
and that's what is changing
anonymous
  • anonymous
thus an "exponential" function
anonymous
  • anonymous
ohhh okay!
anonymous
  • anonymous
so what if we're given the graph and need to find the function? (I have an example)
anonymous
  • anonymous
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
anonymous
  • anonymous
how do we know what f(x) is?
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anonymous
  • anonymous
f(2) = 9, what is f(1)?
anonymous
  • anonymous
2?
anonymous
  • anonymous
that's what it looks like to me... so f(2)/f(1) = base
anonymous
  • anonymous
so 9/2 is the base?
anonymous
  • anonymous
that's what i think
anonymous
  • anonymous
okay, then what's the exponent part?
anonymous
  • anonymous
whoa... wait
anonymous
  • anonymous
what?
anonymous
  • anonymous
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?
anonymous
  • anonymous
I thought it showed that each mark is 1...
anonymous
  • anonymous
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
anonymous
  • anonymous
there are 5 marks to 9... 1 + 2 + 2 + 2 + 2 = 9
anonymous
  • anonymous
besides (9/2)^1 = 9/2 \(\ne\) 2 and (9/2)^2 = 81/4 \(\ne\) 9

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