Use the function f(x)= tan(2x+1) to answer the following
Determine the period (P) and phase shift (PS) of the function
explain what each part would represent in a graph of this function
tan(2x+1) = tan(2(x + 1/2))
since tan(kx) has period π/k, this has period π/2
f(x-k) is shifted to the right by k, so this is shifted left by 1/2
thank you so much!
To determine the period (P) and phase shift (PS) of the function f(x) = tan(2x+1), we need to understand the general form of the tangent function.
The general form of the tangent function is f(x) = A * tan(Bx + C) + D, where A, B, C, and D are constants. In this case, A = 1, B = 2, C = 1, and D = 0 (since they are not given in the question).
1. Period (P):
The period of a function represents the length of one complete cycle or wave. For the tangent function, the period is given by P = π/B.
In our case, B = 2, so the period P = π/2.
This means that the graph of f(x) = tan(2x+1) will complete one cycle every π/2 units along the x-axis.
2. Phase Shift (PS):
The phase shift represents the horizontal shift of the graph, indicating where the graph starts.
In general, for the tangent function with the form f(x) = tan(Bx), the phase shift is given by PS = -C/B.
In our case, B = 2 and C = 1.
So, the phase shift PS = -1/2.
This means that the graph will shift to the left by 1/2 units.
To summarize:
- The period (P) of the function f(x) = tan(2x+1) is π/2, indicating that the graph completes one cycle every π/2 units along the x-axis.
- The phase shift (PS) of the function is -1/2, indicating that the graph will be shifted 1/2 units to the left.
On a graph, the period represents the length of one complete cycle, while the phase shift represents the horizontal displacement of the graph.