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.

- katherinesmith

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- katherinesmith

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- phi

any ideas ?

- katherinesmith

well it shifts to the right and up

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- phi

yes. any numbers ?

- katherinesmith

shifts up 2 and right 1?

- 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

5

- 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

x - 5

- phi

and the new equation is ?

- katherinesmith

\[y = 2^{x - 5} + 2\]

- 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

i think you literally have saved my life

- katherinesmith

i have 3 left

- phi

ok

- 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.

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- katherinesmith

up and to the left?

- phi

definitely

- katherinesmith

left 2 up 1?

- 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

left -1?

- katherinesmith

or -2

- 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

i have no idea.

- phi

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- katherinesmith

2 steps to the left

- 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

okay i understand that.

- phi

so the shifts are 1 up, 1 to the left.

- katherinesmith

\[y = 2^{x + 1} + 1\]

- 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

f(x) = log(x)

- phi

ok, so what is the new equation ?

- katherinesmith

\[f(x) = \log(x + 1) +1\]

- katherinesmith

that is a total guess

- 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

so it would be y = and not f(x) =
?

- phi

if they use f(x), then use the same thing.

- katherinesmith

okay. do you want me to open a new question for the last 2

- phi

yes

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