Asked by Mason
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A waveform is graphed on a coordinate plane. The x-axis ranges from negative pi to Start Fraction 5 pi over 2 End Fraction in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 1 to 3 in increments of 1.
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Determine which function matches the given graph.
(1 point)
Responses
f(x)=sin(2(x−π4))+1
f left parenthesis x right parenthesis equals sine left parenthesis 2 left parenthesis x minus Start Fraction pi over 4 End Fraction right parenthesis right parenthesis plus 1
f(x)=−sin(2(x−π4))+1
f left parenthesis x right parenthesis equals negative sine left parenthesis 2 left parenthesis x minus Start Fraction pi over 4 End Fraction right parenthesis right parenthesis plus 1
f(x)=−sin(12(x−π4))+1
f left parenthesis x right parenthesis equals negative sine left parenthesis Start Fraction 1 over 2 End Fraction left parenthesis x minus Start Fraction pi over 4 End Fraction right parenthesis right parenthesis plus 1
f(x)=−sin(2(x+π4))+1
f left parenthesis x right parenthesis equals negative sine left parenthesis 2 left parenthesis x plus Start Fraction pi over 4 End Fraction right parenthesis right parenthesis plus 1
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All Answers 1
Answered by
GPT-5 mini
AI
f(x) = −sin(2(x − π/4)) + 1
Reason: The midline is y = 1 and the amplitude is 1, so the form is ±sin(2(x−π/4))+1 (vertical shift +1, |a|=1). The period is π so the inside factor is 2. The graph is reflected (peaks where sin would have troughs), so the sine is negative, giving −sin(2(x−π/4))+1.
Reason: The midline is y = 1 and the amplitude is 1, so the form is ±sin(2(x−π/4))+1 (vertical shift +1, |a|=1). The period is π so the inside factor is 2. The graph is reflected (peaks where sin would have troughs), so the sine is negative, giving −sin(2(x−π/4))+1.
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