Graph of the Function $f(x)=\text{tg}\left(x+\frac{\pi}{4}\right)$

Project ID: 
3000000008
SubArea: 
Sine, cosine, tangent and cotangent
Level: 
A
Question: 

Task: Sketch the graph of the function $f(x)=\text{tg}\left(x+\frac{\pi}{4}\right)$.

Student Tom's solution is in the picture. But his sketch is wrong. Can you identify what Tom did wrong? Mark the answer containing only true statements.

Question Image: 
Answer 1: 

Tom determined the asymptotes correctly, but the graph of the function is incorrect. The curve of the given function is increasing between adjacent asymptotes.

Answer 2: 

Tom determined the asymptotes incorrectly. The function is not defined at points $x=\frac{\pi}{2}+k\cdot\pi$, where $k\in\mathbb{Z}$.

Answer 3: 

Tom determined the asymptotes incorrectly. The function is not defined at points $x=-\frac{\pi}{4}+k\cdot\pi$, where $k\in\mathbb{Z}$.

Answer 4: 

Tom determined the asymptotes incorrectly. The function is not defined at points $x=\frac{\pi}{4}+2k\cdot\pi$, where $k\in\mathbb{Z}$.

Correct Answer: 
Answer 1