katherinesmith
  • katherinesmith
graphing question; please help!
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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katherinesmith
  • katherinesmith
1) The red graph (1) is the graph of f(x) = 2x. Describe the transformation of the blue function (2) and write the equation of the graph.
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anonymous
  • anonymous
dont listen to wwesuperstar
katherinesmith
  • katherinesmith
well can someone help me..

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anonymous
  • anonymous
it's -2x
katherinesmith
  • katherinesmith
i have to describe the transformation and write the equation of the graph.
anonymous
  • anonymous
the same x value goes to negative y value so you just should take the negative of function
katherinesmith
  • katherinesmith
that does not help me describe the transformation... and i don't even know if that equation makes sense.
katherinesmith
  • katherinesmith
maybe @jim_thompson5910 can help me
phi
  • phi
The equation is 2^x it looks like they shifted it left by 1, flipped it (multiply by -1) and then shifted up by 3
katherinesmith
  • katherinesmith
but the equation of the first graph is 2^x, so how can it be the same for the second graph?
phi
  • phi
the original is 2^x
phi
  • phi
do you know how to shift a graph to the left by 1 ? you replace x with x+1
katherinesmith
  • katherinesmith
the red graph is the graph of 2^x. so the equation of both graphs is 2^x?
jdoe0001
  • jdoe0001
he's not saying that, he's saying, use 2^x and apply the transformations as explained
phi
  • phi
the red graph is 2^x the blue graph is the red graph shifted left by 1, reflected about the x-axis (multiply by -1) and then shifted up by 3
katherinesmith
  • katherinesmith
so 2x - 1(-1) + 3?
phi
  • phi
can you type that in with ^ and parens to show what is where ?
katherinesmith
  • katherinesmith
i have no idea how to write it.
katherinesmith
  • katherinesmith
i'm fiddling with it and i can't figure it out.
phi
  • phi
you start with 2^x or 2^(x) which is \( 2^x\) shift to the left 1 step means replace x with (x+1) can you replace x with (x+1) ?
jdoe0001
  • jdoe0001
use the whiteboard maybe
katherinesmith
  • katherinesmith
\[2^{x + 1}\]
phi
  • phi
now reflect about the x-axis you now have y= 2^(x+1) reflecting about the x-axis is done by multiplying by -1 (this makes the red curve go negative instead of positive) can you multiply -1 times 2^(x+1) ?
katherinesmith
  • katherinesmith
is it \[y = -2^{x + 1}\]
phi
  • phi
you write \[ -1 \cdot 2^{x+1} \] or just \[ -2^{x+1} \]
katherinesmith
  • katherinesmith
okay i got that
phi
  • phi
finally they shifted up by 3. whatever y value we get from \[ y = -2^{x+1} \] is low by 3 units. add 3 to shift up.
katherinesmith
  • katherinesmith
\[y = -2^{x + 1} + 3 \]
phi
  • phi
yes, that is the answer. as a check, when x= -1 , the blue curve is - 2^0 + 3 = -1 + 3 = 2 when x =0, the blue curve is -2^1 + 3 = -2+3 = 1 and when x =2, the blue curve is -2^3 + 3 = -8+3 = -5 you can check that the blue curve goes through the points (-1,2), (0,1) and (2,-5)
katherinesmith
  • katherinesmith
this actually makes me want to shoot myself because i have like 5 more of these.
phi
  • phi
Does that mean you don't understand what is going on ?
katherinesmith
  • katherinesmith
i understand the equation... somewhat. i don't really understand the transformations. like okay this is the next one: The red graph (1) is the graph of f(x) = 2x. Describe the transformation of the blue function (2) and write the equation of the graph.
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phi
  • phi
you should use the ^ because 2x means 2*x which is different.
katherinesmith
  • katherinesmith
i didn't notice i forgot. normally i'm good with that
phi
  • phi
Just looking at the picture, without going into details, how do you get to the blue curve. It looks like it was shifted to the right, and shifted down.
katherinesmith
  • katherinesmith
okay, i see that. but how do you know how many units right and down it was shifted
phi
  • phi
look at the flat part of the curve (on the left). how far down do you count to get from the red to the blue curve? that will be the shift down (it will be a negative number)
katherinesmith
  • katherinesmith
-6?
phi
  • phi
so that will be your y shift now for the x shift. look at the red curve. it is near zero on the left and then goes up. see where it goes up exactly 1 step ? that happens at x=0 now do the same for the blue curve. at what x does the blue curve go up exactly 1 step ?
katherinesmith
  • katherinesmith
-5
phi
  • phi
that is the y value. what is the x value ?
katherinesmith
  • katherinesmith
4
phi
  • phi
yes. the shift is 4 to the right. that means you replace x with (x-4) (going left/right is confusing.... to shift right 4 steps, you add -4 to the x) can you come up with the new equation, starting with y = 2^x and shifting right 4 steps, and down 6 steps ?
katherinesmith
  • katherinesmith
sike it's 5
katherinesmith
  • katherinesmith
wait no. it is 4. okay let me try
katherinesmith
  • katherinesmith
\[y = 2^{x - 4} - 6\]
phi
  • phi
now do a check. when x=6 what do you get for y with your equation ?
katherinesmith
  • katherinesmith
-2
phi
  • phi
does the blue curve go through the point (6,-2) ?
katherinesmith
  • katherinesmith
yes
phi
  • phi
so that looks good.
katherinesmith
  • katherinesmith
thank god. 4 more. kill me
phi
  • phi
you should make it a new post.
katherinesmith
  • katherinesmith
okay i am.

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