SOLUTION: Give the domain and range for the general functions. Assume A>0. h(x)=A tan (nx-b)

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Question 1084189: Give the domain and range for the general functions. Assume A>0.
h(x)=A tan (nx-b)
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Domain:
The domain is the set of allowed inputs of this function. It is the set of allowed x values we can plug in.
It turns out that tangent is undefined whenever the input is equal 90 degrees, 270 degrees, etc

In general, if the argument is equal to 180k+90, for any integer k, then the result will be undefined.

Set the argument equal to 180k+90 solve for x

So if x is equal to , then n*x-b is equal to 180k+90.

Therefore, the domain is the set of x values such that x is a real number but x cannot equal
Using set builder notation, we'd write that as

where k is any integer.

Range:
The range is the set of all real numbers. Notice how the graph of any tangent function has the graph stretch vertically on forever in both y directions.

Edit: I made the correction. Instead of 90k, it should be 180k+90 assuming you're working in degree mode. Other corrections are based on this. Apologies for any confusion.

Answer by ikleyn(53763) (Show Source):
You can put this solution on YOUR website!
.
The correct answer is:

the domain of the function h(x) = a*tan(nx-b) is the set of all real numbers except those where nx-b = , k = 0, +/-1, +/-2, . . . i.e. except x = , k = 0, +/-1, +/-2, . . .