SOLUTION: If the graph of y=cos(pix)-2 is shifted up by 3 units, left by 1 unit and vertically stretched by a factor of 2, what will be new equation describing it?(explain too please) a) y=

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Question 1078505: If the graph of y=cos(pix)-2 is shifted up by 3 units, left by 1 unit and vertically stretched by a factor of 2, what will be new equation describing it?(explain too please)
a) y= 2cos(pi(x-1)) -5
b) y=cos(2pi(x-1)) +1
c) y=cos(2pix +1)-5
d) y=2 cos(pi(x+1))+1
e) none
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the general formula is:

y = acos(b(x-c))+d

a is the amplitude
b is the frequency
c is the horizontal shift
d is the vertical shift.

your equation is y = cos(pi * x) - 2

shift it up 3 units and it becomes y = cos(pi * x) + 1

shift it to the left 1 unit and it becomes y = cos(pi * (x+1) + 1

stretch it vertically by a factor of 2 and it becomes y = 2 * cos(pi * (x+1)) + 1

my first graph is the original function.

my second graph shifts the function from the first graph up by 3 units.

my third graph shifts the function from the second graph to the left 1 unit.

my fourth graph vertically expands the third graph by a factor of 2.

the fourth graph is your solution.

that looks like your selection d.

note that:

frequency is equal to 2pi / period.

since the frequency of your first graph is pi radians, then the period is 2pi/pi = 2 radians.

you get one complete cycle of the cosine wave in 2 radians as shown on the graph.

in the first graph:

the horizontal range goes from x = 0 to x = 2
the center line is y = -2
the vertical range goes from y = -1 to y = -3

in the second graph:

the horizontal range remains at x = 0 to x = 2
the center line moves up 3 units to y = 1
the vertical range becomes y = 2 to y = 0

this is because the graph has been shifted up 3 units.

in the third graph:

the horizontal range becomes x = -1 to x = 1
the center line remains at y = 1
the vertical range remains at y = 2 to y = 0

this is because the graph has been shifted to the left 1 unit.

in the fourth graph:

the horizontal range remains at x = -1 to x = 1
the center line remains at y = 1
the vertical range becomes y = 3 to y = -1

this is because the vertical range has been multiplied by a factor of 2.

here's a reference that looks pretty complete.

http://www.mathguide.com/lessons2/GraphingTrig.html