How do u graph these without using a graphing calculator?

[gillgill]

How do u graph these without using a graphing calculator?
a) f(x)=3sin2x
b) f(x)=1+cosx

 

[blue_soda025]

Look at what the numbers do to the function.
For a), the amplitude is 3 and the period is pi.
b) Vertical displacement of 1

 

[thepatientmental]

a) To graph f(x)=3sin2x without a graphing calculator, you can use the properties of the sine function to plot points on a coordinate plane. The general form of the sine function is y=sin(x), where x is the angle and y is the value of the function. In this case, we have f(x)=3sin2x, which means the amplitude is 3 and the period is π (since 2x=π when x=π/2).

To graph this function, you can start by plotting points for x=0, π/2, π, 3π/2, and 2π. These correspond to the key points on the graph of the sine function. Then, use the amplitude of 3 to determine the height of the graph at each point. For example, at x=0, the value of the function is 3sin(2(0))=0, so the point (0,0) is on the graph. At x=π/2, the value of the function is 3sin(2(π/2))=3sin(π)=0, so the point (π/2,0) is on the graph.

Continue plotting points and connecting them to create a smooth curve. You can also use the symmetry of the sine function to plot points on the other side of the y-axis. Once all points are plotted and connected, you will have the graph of f(x)=3sin2x.

b) Similarly, to graph f(x)=1+cosx without a graphing calculator, you can use the properties of the cosine function and plot points on a coordinate plane. The general form of the cosine function is y=cos(x), where x is the angle and y is the value of the function. In this case, we have f(x)=1+cosx, which means the amplitude is 1 and the period is 2π.

Start by plotting points for x=0, π/2, π, 3π/2, and 2π. These correspond to the key points on the graph of the cosine function. Then, use the amplitude of 1 to determine the height of the graph at each point. For example, at x=0, the value of the function is 1+cos(0)=1+1=2, so the point (0,2) is on the graph