A sine function has the following key features:
Period = π
Amplitude = 2
Midline: y= −2
y-intercept: (0, -2)
The function is a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the mid-line and the second point must be a maximum or minimum value on the graph closest to the first point.
To graph the given sine function, we can use its given key features and follow these steps:
Step 1: Start by plotting the y-intercept. The y-intercept for the given function is (0, -2), which means the graph passes through the point (0, -2).
Step 2: Since the period of the sine function is π, we can determine that one complete cycle of the function will occur over the interval [0, π].
Step 3: Next, find the maximum or minimum value of the function closest to the first point on the graph. Since the midline is y = -2, the maximum value would be 2 units above the midline and the minimum value would be 2 units below the midline. Since the amplitude of the function is given as 2, the maximum value would be -2 + 2 = 0, and the minimum value would be -2 - 2 = -4.
Step 4: Plot two points on the graph. The first point should be on the midline, which is (0, -2). The second point should be either the maximum value or the minimum value closest to the first point. In this case, the maximum value is (π/2, 0).
Step 5: Now, connect the two points with a smooth wave that passes through the midline. Since the function is a reflection of its parent function over the x-axis, the graph will be reflected below the x-axis.
The completed graph of the sine function with the given key features is shown below:
```
|
2 | x
| x
| x
| x
Midline |- - - - - - - -
-4 | x
| x
| x
| x
|
_______________
0 π/2 π
```
Note: The x-axis represents the values of x, while the y-axis represents the corresponding values of y for the sine function.
we've done a bunch of these.
Why don't you show some work now?