could someone help me please.

State the amplitude and the range of the graph of y= -0.8sinx.
Describe the transformations that are applied to the graph of y=sinx to obtain the graph of y= -0.8sinx.

amplitude is .8

range is from -.8 to .8
transformation is a multiplier of -.8

Of course! Let's break down your questions one by one.

First, let's find the amplitude and range of the graph of y = -0.8sin(x). The amplitude of a trigonometric function is the distance from the midline to the peak or trough of the graph. In this case, the amplitude is 0.8. Since the coefficient in front of the sine function is negative, the graph is reflected vertically, which means it is inverted.

The range of the graph is the set of all possible y-values. For the sine function, the range is usually between -1 and 1. However, since we have multiplied the function by -0.8, the range of this specific graph is between -0.8 and 0.8. Therefore, the range is (-0.8, 0.8).

Next, let's describe the transformations that are applied to the graph of y = sin(x) to obtain the graph of y = -0.8sin(x).

1. Reflection:
The negative sign in front of the function (-0.8sin(x)) causes a reflection about the x-axis. This means that each point on the original graph's y-axis is flipped to the opposite side of the x-axis. This reflection results in an inverted graph compared to the original sine graph.

2. Vertical Stretch:
The coefficient 0.8 in front of sin(x) compresses or stretches the graph vertically. Since the coefficient is less than 1, it causes the graph to be vertically squeezed or compressed. In this case, the graph is vertically stretched by a factor of 0.8.

To summarize, the graph of y = -0.8sin(x) is obtained by reflecting the graph of y = sin(x) about the x-axis and vertically stretching it by a factor of 0.8.