graphing question; please help!

- katherinesmith

graphing question; please help!

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- 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

dont listen to wwesuperstar

- katherinesmith

well can someone help me..

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## More answers

- anonymous

it's -2x

- katherinesmith

i have to describe the transformation and write the equation of the graph.

- anonymous

the same x value goes to negative y value so you just should take the negative of function

- katherinesmith

that does not help me describe the transformation... and i don't even know if that equation makes sense.

- katherinesmith

maybe @jim_thompson5910 can help me

- 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

but the equation of the first graph is 2^x, so how can it be the same for the second graph?

- phi

the original is 2^x

- phi

do you know how to shift a graph to the left by 1 ? you replace x with x+1

- katherinesmith

the red graph is the graph of 2^x. so the equation of both graphs is 2^x?

- jdoe0001

he's not saying that, he's saying, use 2^x and apply the transformations as explained

- 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

so 2x - 1(-1) + 3?

- phi

can you type that in with ^ and parens to show what is where ?

- katherinesmith

i have no idea how to write it.

- katherinesmith

i'm fiddling with it and i can't figure it out.

- 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

use the whiteboard maybe

- katherinesmith

\[2^{x + 1}\]

- 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

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

- phi

you write
\[ -1 \cdot 2^{x+1} \]
or just
\[ -2^{x+1} \]

- katherinesmith

okay i got that

- 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

\[y = -2^{x + 1} + 3 \]

- 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

this actually makes me want to shoot myself because i have like 5 more of these.

- phi

Does that mean you don't understand what is going on ?

- 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

you should use the ^ because 2x means 2*x which is different.

- katherinesmith

i didn't notice i forgot. normally i'm good with that

- 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

okay, i see that. but how do you know how many units right and down it was shifted

- 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

-6?

- 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

-5

- phi

that is the y value. what is the x value ?

- katherinesmith

4

- 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

sike it's 5

- katherinesmith

wait no. it is 4. okay let me try

- katherinesmith

\[y = 2^{x - 4} - 6\]

- phi

now do a check. when x=6 what do you get for y with your equation ?

- katherinesmith

-2

- phi

does the blue curve go through the point (6,-2) ?

- katherinesmith

yes

- phi

so that looks good.

- katherinesmith

thank god. 4 more. kill me

- phi

you should make it a new post.

- katherinesmith

okay i am.

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