Final answer:
To graph the function y = tan(x - π/4) over a one period interval, graph the tangent function and shift it horizontally by π/4 units to the right.
Step-by-step explanation:
To graph the function y = tan(x - π/4) over a one period interval, we first need to understand the properties of the tangent function. The tangent function has a period of π radians, which means it repeats every π units. To graph the function, we can start by graphing one period of the tangent function and then shifting it horizontally by π/4 units to the right.
The graph of the tangent function starts at its asymptote (a vertical line where the function is undefined) and then oscillates between positive and negative values as x increases. The asymptotes occur at x-values that are odd multiples of π/2.
So, to graph the function y = tan(x - π/4) over a one period interval, we can:
- Choose an interval of length π, for example, [0, π]
- Graph the tangent function on this interval, remembering to include the asymptotes at x = π/2 and x = 3π/2
- Shift the graph horizontally by π/4 units to the right