anonymous
  • anonymous
HELP ME PLEASE Which of the following exponential functions goes through the points (1, 6) and (2, 12)? f(x) = 3(2)x f(x) = 2(3)x f(x) = 3(2)−x f(x) = 2(3)−x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ybarrap
  • ybarrap
Plug in x=1 and see if it equals 6 Plug in x=2 and see if it equals 12 Make sense?
anonymous
  • anonymous
not really? can you guide me through it? (xD I dont want to be an answer-hogger/wanter.. I dont want the answer, just explanations :) ) @freckles
anonymous
  • anonymous
Do you understand that coordinates are in the form (x,y)?

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anonymous
  • anonymous
yes. @BMF96
anonymous
  • anonymous
f(x) = y
anonymous
  • anonymous
What don't you understand?
jim_thompson5910
  • jim_thompson5910
If \[\Large f(x) = 7(3)^x\] (for example), then what is the value of f(x) when x = 2? In other words, what is f(2) equal to?
anonymous
  • anonymous
f(2)=441?? #CONFUSED
jim_thompson5910
  • jim_thompson5910
Replace each x with 2 \[\Large f(x) = 7(3)^x\] \[\Large f(2) = 7(3)^2\] \[\Large f(2) = 7(9)\] \[\Large f(2) = 63\] Do you see how I got f(2) to be equal to 63?
jim_thompson5910
  • jim_thompson5910
btw you square first and then you multiply
anonymous
  • anonymous
ok, I forgot that rule :) (like DUHR, Bella, get a grip)
jim_thompson5910
  • jim_thompson5910
Since \(\Large f({\color{red}{2}}) = {\color{blue}{63}}\) from my example, this means the point \(\Large ({\color{red}{x}},{\color{blue}{y}})=({\color{red}{2}},{\color{blue}{63}})\) lies on the function curve of f(x)
anonymous
  • anonymous
okayyy....
jdoe0001
  • jdoe0001
\(f(x)=y= \begin{cases} 3(2)^x\\ 2(3)^x\\ 3(2)^{-x}\\ 2(3)^{-x} \end{cases}\qquad \qquad \begin{array}{llll} x&y \\\hline\\ {\color{brown}{ 1}}&3(2)^{\color{brown}{ 1}}\\ &2(3)^{\color{brown}{ 1}}\\ &3(2)^{-{\color{brown}{ 1}}}\\ &2(3)^{-{\color{brown}{ 1}}}\\ {\color{brown}{ 2}}&3(2)^{\color{brown}{ 2}}\\ &2(3)^{\color{brown}{ 2}}\\ &3(2)^{-{\color{brown}{ 2}}}\\ &2(3)^{-{\color{brown}{ 2}}} \end{array}\)
jim_thompson5910
  • jim_thompson5910
so what ybarrap said at the top, you plug in each x coordinate into each function and see if you get the correct corresponding y coordinates Let's say we pick choice B at random \[\Large f(x) = 2(3)^x\] The first point is (1,6). To test if this point lies on the function f(x) curve, we plug in x = 1 and see if y = 6 pops out \[\Large f(x) = 2(3)^x\] \[\Large f(1) = 2(3)^1\] \[\Large f(1) = 2(3)\] \[\Large f(1) = 6\] It does, so (1,6) is definitely on this curve. How about (2,12)? Let's check \[\Large f(x) = 2(3)^x\] \[\Large f(2) = 2(3)^2\] \[\Large f(2) = 2(9)\] \[\Large f(2) = 18\] Nope. The point (2,18) actually lies on this function curve and NOT (2,12). So we can rule out choice B.
jim_thompson5910
  • jim_thompson5910
So what just happened was that I've proven that the function \(\Large f(x) = 2(3)^x\) does NOT go through both points (1,6) and (2,12).
anonymous
  • anonymous
okay, so its A, C, or D lol.... so lets try to rule out A...
anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
what did you get so far in checking choice A?
anonymous
  • anonymous
that A is, in fact NOT the answer!?
jim_thompson5910
  • jim_thompson5910
if x = 1, then what is f(1) ?
anonymous
  • anonymous
f
anonymous
  • anonymous
Wait, so it IS A!!!!!
jim_thompson5910
  • jim_thompson5910
\[\Large f(x) = 3(2)^x\] \[\Large f(1) = 3(2)^1\] \[\Large f(1) = \underline{ \ \ \ \ \ \ \ } \text{ (fill in the blank)}\]
anonymous
  • anonymous
6
jim_thompson5910
  • jim_thompson5910
and how about f(2)
anonymous
  • anonymous
12
jim_thompson5910
  • jim_thompson5910
Good. Choice A is definitely the answer. As practice, why not go through C and D and eliminate them. With choice C, if x = 1, then what is f(x) equal to?

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