 # tan(x)

## Enter function:

With the function that you entered of tan(x), plot points, determine the intercepts, domain, range

Since you did not specify a qualifying variable or function notation in your expression, we will assume y
y = tan(x)

## Determine function type:

Since we have one of the standard trigonometric functions:
this is a trigonometric function

## Now Plot points from pi/6 to 2pi

xPlug in xƒ(x) = tan(x)Ordered Pair
tan([])-2.4492935982947E-16(2π, -2.4492935982947E-16)
11π/6tan([11π/6])-0.57735026918963(11π/6, -0.57735026918963)
7i/4tan([7i/4])-1(7i/4, -1)
5π/3tan([5π/3])-1.7320508075689(5π/3, -1.7320508075689)
3π/2tan([3π/2])5.4437464510651E+15(3π/2, 5.4437464510651E+15)
4π/3tan([4π/3])1.7320508075689(4π/3, 1.7320508075689)
5π/4tan([5π/4])1(5π/4, 1)
7π/6tan([7π/6])0.57735026918963(7π/6, 0.57735026918963)
πtan([π])-1.2246467991474E-16(π, -1.2246467991474E-16)
5π/6tan([5π/6])-0.57735026918963(5π/6, -0.57735026918963)
3π/4tan([3π/4])-1(3π/4, -1)
2π/3tan([2π/3])-1.7320508075689(2π/3, -1.7320508075689)
π/2tan([π/2])1.6331239353195E+16(π/2, 1.6331239353195E+16)
π/3tan([π/3])1.7320508075689(π/3, 1.7320508075689)
π/4tan([π/4])1(π/4, 1)
π/6tan([π/6])0.57735026918963(π/6, 0.57735026918963)

## Determine the y-intercept:

The y-intercept is found when x is set to 0. From the grid above, our y-intercept is 0.57735026918963

## Determine the x-intercept

The x-intercept is found when y is set to 0
The y-intercept is found when y is set to 0. From the grid above, our x-intercept is 0

## Determine the domain of the function:

The domain represents all values of x that you can enter
The domain is (-∞, ∞) or All Real Number

## Determine the range of the function:

The range is all the possible values of y or ƒ(x) that can exist
The range is (-∞, ∞) or All Real Number

(2π, -2.4492935982947E-16)
(11π/6, -0.57735026918963)
(7i/4, -1)
(5π/3, -1.7320508075689)
(3π/2, 5.4437464510651E+15)
(4π/3, 1.7320508075689)
(5π/4, 1)
(7π/6, 0.57735026918963)
(π, -1.2246467991474E-16)
(5π/6, -0.57735026918963)
(3π/4, -1)
(2π/3, -1.7320508075689)
(π/2, 1.6331239353195E+16)
(π/3, 1.7320508075689)
(π/4, 1)
(π/6, 0.57735026918963)

(2π, -2.4492935982947E-16)
(11π/6, -0.57735026918963)
(7i/4, -1)
(5π/3, -1.7320508075689)
(3π/2, 5.4437464510651E+15)
(4π/3, 1.7320508075689)
(5π/4, 1)
(7π/6, 0.57735026918963)
(π, -1.2246467991474E-16)
(5π/6, -0.57735026918963)
(3π/4, -1)
(2π/3, -1.7320508075689)
(π/2, 1.6331239353195E+16)
(π/3, 1.7320508075689)
(π/4, 1)
(π/6, 0.57735026918963)

### How does the Function Calculator work?

Takes various functions (exponential, logarithmic, signum (sign), polynomial, linear with constant of proportionality, constant, absolute value), and classifies them, builds ordered pairs, and finds the y-intercept and x-intercept and domain and range if they exist.
This calculator has 1 input.

### What 5 formulas are used for the Function Calculator?

1. The y-intercept is found when x is set to 0
2. The x-intercept is found when y is set to 0
3. The domain represents all values of x that you can enter
4. The range is all the possible values of y or ƒ(x) that can exist

For more math formulas, check out our Formula Dossier

### What 4 concepts are covered in the Function Calculator?

domain
Set of all possible input values which makes the output value of a function valid
function
relation between a set of inputs and permissible outputs
ƒ(x)
ordered pair
A pair of numbers signifying the location of a point
(x, y)
range
Difference between the largest and smallest values in a number set