Given the sine function $f(x)\; =\; 3\; \backslash sin\backslash left(2x\; -\; \backslash frac\{\backslash pi\}\{3\}\backslash right)\; +\; 1$, which of the following correctly describes the amplitude, period, phase shift, and vertical shift of its graph?

The amplitude of the sine function $y\; =\; a\; \backslash sin(bx\; +\; c)\; +\; d$ is determined solely by the coefficient $a$, regardless of the values of $b$, $c$, and $d$.

Given the sine function $y\; =\; \backslash sin(x)$, if the graph is transformed so that its amplitude doubles and its period halves, what is the equation of the new sine function?

Match each characteristic or transformation of the sine function graph on the left with its correct description or effect on the right.

Put the following steps in the correct order to graph the sine function $y\; =\; \backslash sin(x)$ over one full period from $0$ to $2\backslash pi$.

Sort each item into the correct category based on their characteristics related to graphing the sine function.

Arrange the key steps in graphing the sine function in the correct order.

Unscramble the letters to find the term that describes the horizontal shift of the sine graph along the x-axis.

Which two of the following statements correctly describe how changes to the amplitude and period affect the graph of the sine function $y\; =\; \backslash sin\; x$? (Select all that apply.)

Given the sine function $f(x)\; =\; 3\; \backslash sin\backslash left(2x\; -\; \backslash frac\{\backslash pi\}\{3\}\backslash right)\; +\; 1$, which of the following statements correctly describe the transformations applied to the parent function $y\; =\; \backslash sin\; x$ when graphing $f(x)$? Select all that apply.