find the period of the function and use the language of transformations to describe how the graph of the…

find the period of the function and use the language of transformations to describe how the graph of the function is related to the graph of y = sin x. y = 8 sin 2x what is the period of the function? π (simplify your answer. use integers or fractions for any numbers in the expression. type an exact answer, using π as needed.) how is the graph of the function related to the graph of y = sin x? choose the correct answer below. a. the graph of y = 8 sin 2x is a horizontal stretch of the graph of y = sin x by a factor of 2 and a vertical stretch by a factor of 8. b. the graph of y = 8 sin 2x is a horizontal shrink of the graph of y = sin x by a factor of 1/2 and a vertical stretch by a factor of 8. c. the graph of y = 8 sin 2x is a horizontal stretch of the graph of y = sin x by a factor of 8 and a vertical stretch by a factor of 2. d. the graph of y = 8 sin 2x is a horizontal shrink of the graph of y = sin x by a factor of 1/8 and a vertical stretch by a factor of 2.

find the period of the function and use the language of transformations to describe how the graph of the function is related to the graph of y = sin x. y = 8 sin 2x what is the period of the function? π (simplify your answer. use integers or fractions for any numbers in the expression. type an exact answer, using π as needed.) how is the graph of the function related to the graph of y = sin x? choose the correct answer below. a. the graph of y = 8 sin 2x is a horizontal stretch of the graph of y = sin x by a factor of 2 and a vertical stretch by a factor of 8. b. the graph of y = 8 sin 2x is a horizontal shrink of the graph of y = sin x by a factor of 1/2 and a vertical stretch by a factor of 8. c. the graph of y = 8 sin 2x is a horizontal stretch of the graph of y = sin x by a factor of 8 and a vertical stretch by a factor of 2. d. the graph of y = 8 sin 2x is a horizontal shrink of the graph of y = sin x by a factor of 1/8 and a vertical stretch by a factor of 2.

Answer

Explanation:

Step1: Recall period - formula for sine function

The general form of a sine - function is $y = A\sin(Bx - C)+D$, and its period is given by $T=\frac{2\pi}{|B|}$. For the function $y = 8\sin(2x)$, $B = 2$. $T=\frac{2\pi}{|2|}=\pi$

Step2: Analyze horizontal transformation

For the function $y=\sin(x)$ to $y = \sin(Bx)$, if $B>1$, it is a horizontal shrink. Here $B = 2$, so the graph of $y=\sin(x)$ is horizontally shrunk by a factor of $\frac{1}{2}$ to get $y=\sin(2x)$.

Step3: Analyze vertical transformation

For the function $y=\sin(2x)$ to $y = A\sin(2x)$, if $A>1$, it is a vertical stretch. Here $A = 8$, so the graph of $y=\sin(2x)$ is vertically stretched by a factor of 8 to get $y = 8\sin(2x)$.

Answer:

What is the period of the function? $\pi$ How is the graph of the function related to the graph of $y=\sin x$? B. The graph of $y = 8\sin(2x)$ is a horizontal shrink of the graph of $y=\sin x$ by a factor of $\frac{1}{2}$ and a vertical stretch by a factor of 8.