Question

4. f(x) = tan(x) – 3
The domain is all real numbers and the range is all real numbers?
Am i correct or wrong?

Answer 1

For range, you are correct! Nice job!!

For domain, please notice that this is tangent, not sine or cosine. For tangent we have vertical asymptotes in the graph.

Answer 2

can you draw the graph for me so i can get a better view ?

Answer 3

okay so what is the domain?

Answer 4

http://www.wolframalpha.com/input/?i=f%28x%29+%3D+tan%28x%29+%E2%80%93+3

Answer 5

Use wolframalpha for your graphs I don't think anyone is going to draw the graph for you

Answer 6

tan(x)-3 has the same domain as tan(x), with which you are probably familiar.

Answer 7

\[\tan(x)=\frac{\sin(x)}{\cos(x)}\] and so as you may not divide by 0, the domain of tangent is all real numbers except those for which
\[\cos(x)=0\]

Answer 8

of course you want an answer in terms of x and not of cos(x) so you could say all real numbers except
\[x=n\pi+\frac{\pi}{2}, n \in \mathbb Z\]