Question

What is the range of y = tan(x) + 2?

Answer 1

my guess is all real numbers > -2. is this correct?

Answer 2

@phi

Answer 3

@jim_thompson5910

Answer 4

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

Answer 5

you'll be able to see it with a graph

Answer 6

i thought the domain was all real numbers but the range was different

Answer 7

the domain is not the set of real numbers, there are restrictions

Answer 8

there are values of x you cannot use

Answer 9

so what would the domain be

Answer 10

doesn't tan go from -inf to + inf ?
adding 2 does not change that

Answer 11

hint: tan(x) = sin(x)/cos(x)

Answer 12

okay, i see what you mean. so how do i figure the restrictions of the domain to find the domain of the function

Answer 13

use my hint and remember that you cannot divide by zero

Answer 14

is 0 the only restriction?

Answer 15

no x = 0 is allowed

Answer 16

oh my god

Answer 17

tan(0) = 0, so that's defined

Answer 18

see a plot
https://www.wolframalpha.com/input/?i=plot++tan+x

Answer 19

then how the heck do i find the domain.

Answer 20

\[
\cos(x)\neq 0
\]

Answer 21

you need to find out when cos(x) = 0 is true

Answer 22

that way, you'll know which values of x to exclude from the domain

Answer 23

how do i find that out...

Answer 24

use the unit circle

Answer 25

look for points on the unit circle that have an x coordinate of 0

then record the angle

Answer 26

90 degrees and 270 degrees

Answer 27

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

Answer 28

so the domain is the set of all real numbers x, but x cannot equal 90+180n where n is any integer

Answer 29

this is assuming x is in degrees

Answer 30

okay. thank you for the help

Answer 31

yw