A sine function has the following key features:
Period = 4
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not 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 midline and the second point must be a maximum or minimum value on the graph closest to the first point.
pleeeaseee help
y = 1 + 4 sin(π/2 x)
Should be no problem. You know the 1st max will be 1/4 period from the start of the curve at (0,1), at (1,5)
The Mid-Line and intercept is (0,1) or 1
So the first dot is on (0,1)
Your amplitude is 4 so that mean their are 4 spaces in between 1 and 5.
And your period is 4 so your lines minimum should hit 4 if not near it.
So the second dot is on (1,5)
Your answer is 1:(0,1) - 2:(1,5)
(0,1) - (1,5) is correct I took the test
To graph the given sine function, we can follow these steps:
Step 1: Determine the vertical shift (midline):
The midline is given as y = 1. This tells us that the center of the graph will be shifted vertically 1 unit upward from the x-axis.
Step 2: Determine the amplitude:
The amplitude is given as 4. This means the graph will oscillate between 1 (the midline) and 5 (1 + 4).
Step 3: Determine the period:
The period is given as 4. The period of a sine function is the distance between two consecutive maxima or minima. In this case, the function completes one full oscillation in 4 units along the x-axis.
Step 4: Find the phase shift (horizontal shift):
Since no phase shift is given, we assume the function starts at the origin (0, 0).
Step 5: Determine the y-intercept:
The y-intercept is given as (0, 1), which means the graph intersects the y-axis at y = 1.
Now, let's plot the points on the graph based on the given information step by step:
1. Start with the midline: Plot the point (0, 1) since it lies on the midline.
2. Find the maximum or minimum value closest to the first point: Since the amplitude is positive, the first point after the midline will be a maximum value. To determine the x-value, we divide the period by 4: 4 / 4 = 1. This means we move 1 unit to the right from the midline. So plot the second point at (1, 5).
3. Use the symmetry of the sine function:
Since the given sine function is not reflected over the x-axis, we can use the symmetry property to determine the remaining points. This means that for every point (x, y) on the graph, there will be a corresponding point (-x, y) on the other side of the y-axis.
4. Continue plotting points:
Now that we have the first two points, we can use the period to determine the remaining points. Since the period is 4, we can calculate the next point by moving 4 units to the right from the second point (1, 5). This gives us the third point at (5, 1). Then, we find the fourth point by moving 4 units to the right from the third point, which gives us (9, 5). The pattern continues as we keep moving 4 units to the right from each point and plot the corresponding point on the other side.
Once you have plotted several points, you can use them to sketch the graph of the sine function. Remember that the graph will repeat itself every 4 units due to the period.