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my guess is all real numbers > -2. is this correct?
the range of y = tan(x) is the set of all real numbers this is also true for y = tan(x) + 2 because shifting it up or down doesn't change the range
you'll be able to see it with a graph
i thought the domain was all real numbers but the range was different
the domain is not the set of real numbers, there are restrictions
there are values of x you cannot use
so what would the domain be
doesn't tan go from -inf to + inf ? adding 2 does not change that
hint: tan(x) = sin(x)/cos(x)
okay, i see what you mean. so how do i figure the restrictions of the domain to find the domain of the function
use my hint and remember that you cannot divide by zero
is 0 the only restriction?
no x = 0 is allowed
oh my god
tan(0) = 0, so that's defined
see a plot https://www.wolframalpha.com/input/?i=plot++tan+x
then how the heck do i find the domain.
\[ \cos(x)\neq 0 \]
you need to find out when cos(x) = 0 is true
that way, you'll know which values of x to exclude from the domain
how do i find that out...
use the unit circle
look for points on the unit circle that have an x coordinate of 0 then record the angle
90 degrees and 270 degrees
so this means that x cannot be 90 or x cannot be 270 in general, x cannot be equal to 90+180n where n is any integer
so the domain is the set of all real numbers x, but x cannot equal 90+180n where n is any integer
this is assuming x is in degrees
okay. thank you for the help