SOLUTION: 2. Describe what the graph of f(x) = -sin(3x - 𝝿) - 2 would look like? Address all numerical elements and their effects on the parent function.

Algebra ->  Trigonometry-basics -> SOLUTION: 2. Describe what the graph of f(x) = -sin(3x - 𝝿) - 2 would look like? Address all numerical elements and their effects on the parent function.      Log On


   



Question 1205931: 2. Describe what the graph of f(x) = -sin(3x - 𝝿) - 2 would look like? Address all numerical elements and their effects on the parent function.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Describe what the graph of
f%28x%29+=+-sin%283x+-+pi%29+-+2
f%28x%29+=+-1%2Asin%283%28x+-+pi%2F3%29%29+-+2
this graph is of the form f%28x%29=A%2Asin%28Bx-C%29%2BD where A=abs%28-1%29, B=3,C=pi%2F3, D=-2

amplitude: 1
period: 2pi%2F3
phase shift: pi%2F3+ to the right
vertical shift: -2+(2 units down)


Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Describe what the graph of f(x) = -sin(3x - 𝝿) - 2 would look like?
Address all numerical elements and their effects on the parent function.
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        The solution/answer by @MathLover1 in not completely correct.
        I came to fix an error in her solution.


Given function  f(x) = -sin%283x-pi%29-2  is IDENTICAL to / (is the same as)

                f(x) = sin%283x%29+-2.


The parent finction is  a(x) = sin(x).


Amplitude of f(x) is 1.


Period of f(x) is 2pi%2F3.


Phase shift of f(x) is  0  (zero).


Vertical shift is  -2  (2 units down).

Solved.

Find the difference between my solution/answer and solution/answer by @MathLover1.

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This problem is a  TRAP :   it has a huge underwater stone for unexperienced reader.

The sign  "-"  (minus)  before sine and the shift by  pi  in the argument
mutually annihilate each other,  so the final function,  actually,  has no shift (!)

The meaning of the problem is to teach a reader recognizing
such traps to avoid falling into them in the future.