Question

Use the table to answer the question.



The table lists values of a sine function at intervals of π2
. Given the values, identify the equation of the function.

(1 point)
Responses

f(x)=sinx+π4
f(x)=sinx+π4

f(x)=sin(x+π4)
f of x is equal to sine of open paren x plus pi over 4 close paren

f(x)=sin(x+π2)
f of x is equal to sine of open paren x plus pi over 2 close paren

f(x)=sin(x−π4)
f of x is equal to sine of open paren x minus pi over 4 close paren
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Answer 1

f(x) = sin(x + π/4)

Reason: evaluating at x = 0, π/2, π, 3π/2 gives sin(π/4)=√2/2, sin(3π/4)=√2/2, sin(5π/4)=-√2/2, sin(7π/4)=-√2/2, which matches the table. The vertical-shift option (sin x + π/4) is impossible because it would move values outside [−1,1].