Answer:
To graph the function f(x) = -4cosx + 3, we need to follow these steps:
1. Determine the amplitude, period, and phase shift of the function.
- The amplitude is the coefficient of cosx, which is 4 in this case.
- The period is the same as the period of cosx, which is 2π.
- There is no phase shift since the argument of cosx is just x.
2. Plot some points for one period of the function.
- Let's plot points for 0 ≤ x ≤ 2π.
- When x = 0, f(0) = -4cos(0) + 3 = -4(1) + 3 = -1
- When x = π/2, f(π/2) = -4cos(π/2) + 3 = -4(0) + 3 = 3
- When x = π, f(π) = -4cos(π) + 3 = -4(-1) + 3 = 7
- When x = 3π/2, f(3π/2) = -4cos(3π/2) + 3 = -4(0) + 3 = 3
- When x = 2π, f(2π) = -4cos(2π) + 3 = -4(1) + 3 = -1
3. Plot the points on the coordinate plane and connect them with a smooth curve.
4. Label the axes and graph:
8|
7| *
6|
5|
4|
f(x) 3| * *
2|
1|
0| *
-1|* *
-2|
-3|
-4|
-5|
|_______________________________________
0 π/2 π 3π/2 2π x
The graph shows one complete period of the function f(x) = -4cosx + 3, with the x-axis representing the input values and the y-axis representing the output values of the function. The graph has an amplitude of 4, a period of 2π, and is shifted vertically upward by 3 units from the cosine function.
Step-by-step explanation: