Using h(x)=−2sinx, find the y-values in the second row of the table by substituting each x-value into the function. Which of the following is the graph of h(x)?
x −3π2 −π2 π2 3π2
f(x) (1 point)
Responses
A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 2 to 2 in increments of 1.
Image with alt text: A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 2 to 2 in increments of 1.
A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 2 to 2 in increments of 1.
Image with alt text: A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 2 to 2 in increments of 1.
A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 2 to 2 in increments of 1.
Image with alt text: A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 2 to 2 in increments of 1.
A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 2 to 2 in increments of 1.
Image with alt text: A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 2 to 2 in increments of 1.
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Based on the given function h(x) = -2sin(x), we can substitute the x-values from the second row of the table (-3π/2, -π/2, π/2, 3π/2) into the function to find the corresponding y-values.
When x = -3π/2,
h(-3π/2) = -2sin(-3π/2) = -2(-1) = 2
When x = -π/2,
h(-π/2) = -2sin(-π/2) = -2(1) = -2
When x = π/2,
h(π/2) = -2sin(π/2) = -2(1) = -2
When x = 3π/2,
h(3π/2) = -2sin(3π/2) = -2(-1) = 2
The y-values in the second row of the table are 2, -2, -2, and 2.
Looking at the options provided, the correct graph of h(x) is the first image described as "A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of pi/2. The y-axis ranges from negative 2 to 2 in increments of 1."