Graph f (x) = 3cos (4pix -pi/2) -2
wolframalpha is your friend. See
http://www.wolframalpha.com/input/?i=3cos+(4pix+-pi%2F2)+-2
f(x) = 3cos(4pi(x - 1/8) -2
So, it is just the graph of cos(x)
shrunk horizontally by a factor of 4pi
shifted right by 1/8
stretched vertically by 3
shifted down 2
Thank you
To graph the function f(x) = 3cos(4πx - π/2) - 2, we can follow these steps:
1. Determine the period:
The period of the function is given by the formula T = 2π/b, where b is the coefficient of x inside the cosine function. In this case, b = 4π, so the period is T = 2π/(4π) = 1/2.
2. Find the amplitude:
The amplitude of the function is the coefficient in front of the cosine function, which in this case is 3.
3. Determine the phase shift:
The phase shift is given by the formula C = d/b, where d is the constant term inside the cosine function. In this case, d = -π/2 and b = 4π. So the phase shift is C = (-π/2) / (4π) = -1/8.
4. Plot key points on the graph:
To plot the graph, you can start by finding some key points within one period. Since the period is 1/2 and there are 2π radians in a full period, you can divide the period into equal sections to find key points. For example, you can choose values like x = 0, x = 1/8, x = 1/4, etc.
5. Calculate the corresponding y-values:
Substitute the chosen x-values into the function f(x) = 3cos(4πx - π/2) - 2 to find the corresponding y-values.
6. Plot the points and connect them:
Once you have obtained the coordinates for the key points, plot them on the graph. Use them to draw a smooth curve that represents the function.
7. Repeat the pattern:
Since the cosine function repeats itself after one period, you can repeat the pattern of the graph in both directions (to the left and right) to complete the graph.
By following these steps, you can accurately graph the function f(x) = 3cos(4πx - π/2) - 2.