Question

The movement of the progress bar may be uneven because questions can be worth more or less (includingWhich of the following functions is represented by the graph below?2MA2/TT3/TTOy=sin 3x y = 4 sin 2xy = 4 sin(x) y = 2 sin 4x

Answer 1

Answer: $y\text{ = 4 sin\lparen2x\rparen \lparen2nd option\rparen}$

Explanation:

Given:

A sine function graph

To find:

the function that represents the graph

To determine the correct function, we will apply the sine function formula:

$\begin{gathered} y\text{ = Asin\lparen Bx + C\rparen +}D \\ where\text{ A}=\text{ amplitude} \\ B=\text{ }\frac{2\pi}{period} \\ C=phase\text{ shift} \\ D\text{ = vertical shift} \end{gathered}$$\begin{gathered} A\text{ = distance between origin and max = 4} \\ \\ Period\text{ = \pi} \\ B=\text{ }\frac{2π}{π} \\ B\text{ = 2} \\ \\ C=\text{ no phase shift = 0} \\ D\text{ = no vertical shift = 0} \end{gathered}$

Substitute the values into the formula:

$\begin{gathered} y\text{ = 4}sin(2x\text{ + 0\rparen +}0 \\ \\ y\text{ = 4 sin\lparen2x\rparen \lparen2nd option\rparen} \end{gathered}$