katherinesmith
  • katherinesmith
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.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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katherinesmith
  • katherinesmith
1 Attachment
phi
  • phi
any ideas ?
katherinesmith
  • katherinesmith
well it shifts to the right and up

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phi
  • phi
yes. any numbers ?
katherinesmith
  • katherinesmith
shifts up 2 and right 1?
phi
  • phi
yes, up 2. but to the right more than 1 step. if you shifted the blue curve down two, its left part would match the red, but it curves up much later. Find the spot where the red curve first hits y=+1 now find the same spot on the blue curve where it goes up 1 step. what x is that ?
katherinesmith
  • katherinesmith
5
phi
  • phi
yes. the red curve is at x=0 when it reaches y up by 1 step. the blue curve is at x=5 when it goes up by 1 step. that is 5 units to the right. so your shifts are 2 up and 5 to the right how do you do a 5 to the right ? you replace x with ?
katherinesmith
  • katherinesmith
x - 5
phi
  • phi
and the new equation is ?
katherinesmith
  • katherinesmith
\[y = 2^{x - 5} + 2\]
phi
  • phi
as a check, when x=6, the blue curve has y= 4 checking: 2^(6-5) +2 = 2^1 +2 = 2+2= 4. looks good.
katherinesmith
  • katherinesmith
i think you literally have saved my life
katherinesmith
  • katherinesmith
i have 3 left
phi
  • phi
ok
katherinesmith
  • katherinesmith
The red graph (1) is the graph of f(x) = log(x). Describe the transformation of the blue function (2) and write the equation of the graph.
1 Attachment
katherinesmith
  • katherinesmith
up and to the left?
phi
  • phi
definitely
katherinesmith
  • katherinesmith
left 2 up 1?
phi
  • phi
it is up 1. if you are having trouble with the left/right amount. first apply the up 1 shift to the red curve. at a few points. then see if you can see how far the blue curve is shifted right or left
katherinesmith
  • katherinesmith
left -1?
katherinesmith
  • katherinesmith
or -2
phi
  • phi
yes , though I would say shifted -1 or shifted left (but not both) notice if you move the point (1,0) on the red curve up 1, you get (1,1) now how far do you move left to get to the blue curve at (0,1) ?
katherinesmith
  • katherinesmith
i have no idea.
phi
  • phi
|dw:1377722564729:dw|
katherinesmith
  • katherinesmith
2 steps to the left
phi
  • phi
do you see the point (1,0) ? the red curve goes through that point now shift that point up 1 step. you will be at point (1,1) now count steps to the left until you reach a point on the blue curve. you should count 1 step to the left, reaching the point (0,1) on the blue curve.
katherinesmith
  • katherinesmith
okay i understand that.
phi
  • phi
so the shifts are 1 up, 1 to the left.
katherinesmith
  • katherinesmith
\[y = 2^{x + 1} + 1\]
phi
  • phi
except the red curve is not 2^x (notice it does not match your other problems) do they tell you the equation for the red equation ?
katherinesmith
  • katherinesmith
f(x) = log(x)
phi
  • phi
ok, so what is the new equation ?
katherinesmith
  • katherinesmith
\[f(x) = \log(x + 1) +1\]
katherinesmith
  • katherinesmith
that is a total guess
phi
  • phi
it follows the rule: -1 shift means x+1 shift up means add +1 y= log(x+1) + 1 as a check, when x=0 you get log(1)+1= 0+1= 1 which matches the blue curve.
katherinesmith
  • katherinesmith
so it would be y = and not f(x) = ?
phi
  • phi
if they use f(x), then use the same thing.
katherinesmith
  • katherinesmith
okay. do you want me to open a new question for the last 2
phi
  • phi
yes

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