Graph the function y=3 sin x +1
By looking at the function, we can tell it has an amplitude of 3 and a period of 2π. Furthermore, it is shifted up one unit.
To graph, we first move the midline of the parent function up by 1.
To graph, we first move the midline of the parent function up by 1.
Since the amplitude is 3, the graph will reach a max 3 units above the midline and a min 3 units below.
To find the intervals of every point, we divide the period by 4. 2π/4 = π/2
The points have intervals of π/2.
When we consider the pattern that positive sine graphs have, we can plug in the points easily.
The y-coordinates of sine graphs in one period (starting from the initial point) go from midline to max to midline to min and back to the midline.
Then connect the points with a curve.
The points have intervals of π/2.
When we consider the pattern that positive sine graphs have, we can plug in the points easily.
The y-coordinates of sine graphs in one period (starting from the initial point) go from midline to max to midline to min and back to the midline.
Then connect the points with a curve.
The graph of y=3 sin x +1 in two periods.
Graph the function y=2 sin 2x +2
By looking at the function, we can see the function has an amplitude of 2, a period of π, and a vertical shift of 2 units up.
First, move the midline of the parent function up 2.
First, move the midline of the parent function up 2.
With an amplitude if 2, the max will be 2 units above the midline and min will be 2 units below.
To find intervals of each point we divide the period by 4. The interval of each point is π/4.
Next, we consider the pattern of every positive sin graph and plot the points.
Next, we consider the pattern of every positive sin graph and plot the points.
The graph of y=2 sin 2x +2 in four periods.
Graph the function y= -3 cos x-1
By looking at the function, we can see it has an amplitude of 3, a period of 2π and is shifted down one unit. We also see that it is flipped across the x-axis because of the negative in front of the coefficient affecting cos.
First we need to place the initial point and set the midline. To find the initial point, we multiply 1 by -3 and then subtract 1 to get -4.
Since we know the amplitude is 3, we know the max and min will be 3 units from the midline.
To find the interval of each point we divide the period (2π) by 4 to get π/4.
Consider the pattern of cosine graphs to plot points and graph the curve.
Consider the pattern of cosine graphs to plot points and graph the curve.
Graph of y=-3 cos x-1 in two periods