SOLUTION: without graphing determine the amplitude, period, domain, and range of the function of the function y=-2.3sin (5x)+7

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Question 1141495: without graphing determine the amplitude, period, domain, and range of the function of the function y=-2.3sin (5x)+7
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52852) (Show Source):
You can put this solution on YOUR website!
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The amplitude is 2.3. The period is . The domain is the set of all real numbers. The range is [7-2.3,7+2.3] = [4.7,9.3].

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the basic formula is y = a * sin(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=-2.3sin (5x)+7

the amplitude is 2.3

the frequency is 5

the vertical displacement is 7

the period is equal to 360 degrees / the frequency.
that makes the period equal to 360 / 5 = 72 degrees.

since the vertical displacement is 7, the center line of the sine wave is at y = 7.

this makes the range of the sine wave equal to 7 - 2.3 to 7 + 2.3.

that makes it equal to 4.7 <= y <= 9.3.

the domain is all real values of x, since there are no restrictions on the value of x.

that makes the domain - infinity < x < + infinity.

all this was done without graphing.

however, to confirm whether the information supplied is correct, i drew some graphs that are shown below.

the graph confirms what i gold you up top.

the period is 72 degrees.
the frequency is 5
the amplitude is 2.3
the range is y = 4.7 to 9.3
the center line is y = 7
the domain is all real values of x.
the sine wave repeats every 72 degrees.
the domain would be 0 <= x <= 72 plus or minus k * 72, where k is a positive integer.
that makes the domain all real values of x because the value of x goes infinitely on to the right or to the left of the basic period of 0 to 72 degrees.