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The sine function 𝑓(𝑥)=sin⁡(𝑥) is reflected in the 𝑥-axis.Which of these transformations would give the same result on the sine graph?

Question

The sine function 𝑓(𝑥)=sin⁡(𝑥) is reflected in the 𝑥-axis.Which of these transformations would give the same result on the sine graph?

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Solution

The transformation that would give the same result on the sine graph when the sine function 𝑓(𝑥)=sin⁡(𝑥) is reflected in the 𝑥-axis is 𝑓(𝑥)=-sin⁡(𝑥). This is because reflecting a function in the x-axis changes the sign of the output values, which in the case of the sine function, changes sin(𝑥) to -sin(𝑥).

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