Question

explain how the graph of y=-2sin(x)-1 differs from the parent function. Make sure to compare key points used for graphing

Answer 1

You can obtain the graph of the function y=-2sinx-1 from the graph of the function y=sinx making such transformations:
1. the multiplication by -2 increases y value twice and then symmetrically reflects the graph y=2sinx about the x-axis;
2. adding -1 to the y=-2sinx you translate the graph 1 unit down.

On the added picture black line is a graph of y=sinx and red line is a graph of y=-2sinx-1.

Check:
1. When x=0, y=-2sin0-1=-1;
2. When
`x= (3\pi)/(2)`, then
`y=-2\sin (3\pi)/(2) -1=-2(-1)-1=2-1=1`.

Answer 2

You need to include:

The graph of y = –2sin(x) – 1 is the graph of the parent function stretched vertically by a factor of 2, reflected over the x-axis, and shifted 1 unit down.

The maximum of the parent function is 1, the minimum is –1, and the amplitude is 1.

The maximum of y = –2sin(x) – 1 is 1, the minimum is –3, and the amplitude is 2.

Explanation:

Correct on edge 2021!