Question

graphing question; please help!

Answer 1

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.

Answer 2

dont listen to wwesuperstar

Answer 3

well can someone help me..

Answer 4

it's -2x

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

maybe @jim_thompson5910 can help me

Answer 9

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

Answer 10

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

Answer 11

the original is 2^x

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

i have no idea how to write it.

Answer 19

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

Answer 20

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) ?

Answer 21

use the whiteboard maybe

Answer 22

\[2^{x + 1}\]

Answer 23

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) ?

Answer 24

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

Answer 25

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

Answer 26

okay i got that

Answer 27

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.

Answer 28

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

Answer 29

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)

Answer 30

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

Answer 31

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

Answer 32

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.

Answer 33

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

Answer 34

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

Answer 35

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.

Answer 36

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

Answer 37

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)

Answer 38

-6?

Answer 39

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 ?

Answer 40

-5

Answer 41

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

Answer 42

4

Answer 43

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 ?

Answer 44

sike it's 5

Answer 45

wait no. it is 4. okay let me try

Answer 46

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

Answer 47

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

Answer 48

-2

Answer 49

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

Answer 50

yes

Answer 51

so that looks good.

Answer 52

thank god. 4 more. kill me

Answer 53

you should make it a new post.

Answer 54

okay i am.