Question

Sketch two periods of the graph of the function p(x)=tan(x−π4)

. Identify the stretching factor, period, and asymptotes. Enter the exact answers. For the number π
, either choose π
from the bar at the top or type in Pi (with a capital P).
Stretching factor =1. Period: P= Pi. Enter the asymptotes of the function on the domain [−P,P]. To enter π , type Pi. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter.
Asymptotes: x=

Answer 1

To sketch two periods of the graph of the function p(x) = tan(x - π/4), we need to shift the graph of the tangent function to the right by π/4 units. The vertical asymptotes are shifted as well.

Step-by-step explanation:

To sketch the graph of the function p(x) = tan(x - π/4), we can start by graphing one period of the basic tangent function y = tan(x). The period of the tangent function is π, and there are vertical asymptotes at every interval of π. To sketch two periods of the graph for the function p(x) = tan(x - π/4), we need to shift the graph of the tangent function to the right by π/4 units. This will move the vertical asymptotes as well as the points on the graph.

Stretching factor: 1 (there is no stretching factor for the tangent function)

Period: P = π (period of the tangent function)

Asymptotes: x = π/4, x = 5π/4 (one period to the right of the original asymptotes)