Question

the graph (1) is the graph of f(x)=2^x . describe the transformation of the blue function (2) and write the equation of the graph .

Answer 1

Hint: If you are moving from red to blue, then you are moving 5 units to the right and 2 units up

Answer 2

thanks:) what would the equation be ??

Answer 3

the red graph is 2^x

if you shift it 5 units to the right, then you replace x with (x-5)

if you shift 3 units up, then you just add on +3

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So that means

2^x

turns into

2^(x-5) + 3

Answer 4

So if f(x) = 2^x (red graph)

then g(x) = 2^(x-5) + 3 (blue graph)

Answer 5

thank you sooooo much :)

Answer 6

you're welcome

Answer 7

maybe you can help me with the other similar questions

Answer 8

sure, i can do a few more

Answer 9

the red graph (1)is the graph of f(x)=log(x). describe the tranasformation of the blue function and write the equation of the graph.

Answer 10

you are shifting the red graph 5 units to the right and 5 units up to get the blue graph

Answer 11

So

f(x)=log(x).

turns into

f(x)=log(x-5) + 5

using the same rules described above

Answer 12

I meant to write g(x) = log(x-5) + 5

Answer 13

and thats for the blue graph right ?

Answer 14

correct

Answer 15

red ----> blue

start with red, go to blue

Answer 16

okay :) oneeeee more question ! :)

Answer 17

ok

Answer 18

same thing but diffrent graph

Answer 19

you have to reflect over the x axis, then move it down 3 units

Answer 20

okay and the equation for the blue graph ?

Answer 21

the original is f(x) = log(x)

you reflect it over the x axis to get y = -log(x)

then you move it down 3 units to get y = -log(x) - 3

So the blue graph is g(x) = -log(x) - 3

Answer 22

okay thanks again :)

Answer 23

np

Answer 24

do you know how to do the unit circle stuff

Answer 25

what do you mean

Answer 26

like this

Answer 27

ok something like would be very helpful to have in your notes

http://www.regentsprep.org/Regents/math/algtrig/ATT5/600px-Unit_circle_angles_svg.jpg

Answer 28

hopefully the unit circle is somewhat familiar to you

Answer 29

yeah i have it but i dont understand how to do it

Answer 30

well any point that is on the unit circle is the point (x,y)

where

x = cos(theta)

y = sin(theta)

theta = angle

Answer 31

so the point (1/2, sqrt(3)/2) means


cos(60) = 1/2
sin(60) = sqrt(3)/2

since this point is at the place where the angle is 60 degrees