Question

The following functions f and g are periodic. You
can get the graph of g by changing the amplitude
and period of f, and then applying a translation.
Find function g(x) in terms of f(x).

Answer 1

Here are the graphs I have to work with.

Answer 2

@myininaya, @quickstudent, @Compassionate, @Hero, @triciaal I need help on this

Answer 3

@triciaal by any chance would there be a way of doing this because my issue is knowing where and what to start

Answer 4

I am not really sure.
what I am thinking of is finding the function f(x) and identifying the changes to get it to g(x).
f(x) max (pi/2,1) min (3/2*pi, -1) ,(0, 0), (2*pi, 0), (5/2pi. 1)

Answer 5

g(x) (3/4pi, 0), (7/2pi 0)
max 3, min 0

Answer 6

for a given point on f(x) look at the corresponding point on g and how it has "moved"

Answer 7

minimum g(x)= 0

Answer 8

although for the question would I have to show a new translated graph or just use the f(x) graph (the picture) and draw the transition?

Answer 9

@campbell_st i need assistance

Answer 10

well f(x) = sin(x)

g(x) has a period of pi...

so the period is found using

\[period = \frac{2\pi}{b}\]

so b = 2

g(x) seems to have an amplitude of 3... and is centred on 1.5

so find mine

g(x) = 3sin(2x) + 1.5

hope it helps

Answer 11

I think the amplitude of g(x) is 1.5 and

\(\large g(x) = 1.5f(2x) + 1.5\)

Answer 12

dang... amplitude should be 1.5

so I'd say

g(x) = 1.5sin(2x) + 1.5

Answer 13

so technically its just asking me to write an equation to find g(x).

Answer 14

well its asking you to find the equation of g(x) in terms of f(x)

Answer 15

My first thought in my head was "I think I need to draw the translation for this."

Answer 16

but basically this equation is only for g(x)

Answer 17

its a case of using your knowledge to get the equation... look at the period... and the amplitude... and the fact its been shifted up...

Answer 18

@zepdrix

Answer 19

@aaronq