question 30 (1 point) for the function y = 2 sin(x + 30°), the axis is at... x = 2 y = 2 y = -5 x = -5

Explanation:

Step1: Recall sine - function property

The general form of a sine function is $y = A\sin(Bx - C)+D$. For the function $y = 2\sin(x + 30^{\circ})$, which can be written as $y=2\sin(x-(- 30^{\circ}))+0$, the mid - line (axis) of the sine function $y = A\sin(Bx - C)+D$ is given by $y = D$.

Step2: Identify the value of D

In the function $y = 2\sin(x + 30^{\circ})$, $D = 0$. But among the given options, we note that for a sine - type function, the axis is a horizontal line of the form $y = k$. Since there is no $y = 0$ option, and the amplitude is 2, the function oscillates above and below the mid - line. The mid - line of the basic sine function $y=\sin x$ is $y = 0$, and for $y = 2\sin(x + 30^{\circ})$, the axis is still a horizontal line. The value of the axis of the sine function $y = A\sin(Bx - C)+D$ is determined by the vertical shift $D$. Here $D = 0$, but considering the nature of the options and the fact that the axis of a sine function is a horizontal line, we know that the axis of the function $y = 2\sin(x+30^{\circ})$ is a horizontal line and not a vertical line.

Answer:

None of the above options are correct. The axis of the function $y = 2\sin(x + 30^{\circ})$ is $y = 0$. If we assume there is an error in the options and we consider the general concept of the axis of a sine - type function being a horizontal line, and we have to choose from the given options, we note that the axis of a sine function is a horizontal line (not a vertical line like $x = 2$ or $x=-5$). Since the function $y = 2\sin(x + 30^{\circ})$ has no vertical shift other than the default mid - line of the sine function, and among the horizontal line options $y = 2$ and $y=-5$ are incorrect as the mid - line of $y = 2\sin(x + 30^{\circ})$ is $y = 0$. But if we must choose from the given options, none of them are correct for the axis of the function $y = 2\sin(x + 30^{\circ})$.