Use the table to answer the question. x 0 3π4 3π2 9π4 3π f(x) 1 0 −1 0 1 Write the equation of the periodic function represented in the following table. (1 point) Responses f(x)=sin(2x3) f left parenthesis x right parenthesis equals sine left parenthesis Start Fraction 2 x over 3 End Fraction right parenthesis f(x)=cos(2x3) f left parenthesis x right parenthesis equals cosine left parenthesis Start Fraction 2 x over 3 End Fraction right parenthesis f(x)=cos(x3) f left parenthesis x right parenthesis equals cosine left parenthesis Start Fraction x over 3 End Fraction right parenthesis f(x)=sin(x3)
To determine the equation of the periodic function represented in the table, we need to analyze the pattern of the values of x and f(x).
From the table, we can see that the function goes through one complete cycle from x = 0 to x = 9π/4.
The function starts at f(x) = 1 when x = 0 and repeats when x increases by a multiple of 9π/4.
Therefore, the function can be represented as f(x) = sin(x/3).
The correct answer is:
f(x) = sin(x/3)