sec(x) ·

21 Jul 2024, 00:00

Enter function:

With the function that you entered of sec(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 = sec(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

x	Plug in x	ƒ(x) = sec(x)	Ordered Pair
2π	sec([2π])	1	(2π, 1)
11π/6	sec([11π/6])	1.1547005383793	(11π/6, 1.1547005383793)
7i/4	sec([7i/4])	1.4142135623731	(7i/4, 1.4142135623731)
5π/3	sec([5π/3])	2	(5π/3, 2)
3π/2	sec([3π/2])	-5.4437464510651E+15	(3π/2, -5.4437464510651E+15)
4π/3	sec([4π/3])	-2	(4π/3, -2)
5π/4	sec([5π/4])	-1.4142135623731	(5π/4, -1.4142135623731)
7π/6	sec([7π/6])	-1.1547005383793	(7π/6, -1.1547005383793)
π	sec([π])	-1	(π, -1)
5π/6	sec([5π/6])	-1.1547005383793	(5π/6, -1.1547005383793)
3π/4	sec([3π/4])	-1.4142135623731	(3π/4, -1.4142135623731)
2π/3	sec([2π/3])	-2	(2π/3, -2)
π/2	sec([π/2])	1.6331239353195E+16	(π/2, 1.6331239353195E+16)
π/3	sec([π/3])	2	(π/3, 2)
π/4	sec([π/4])	1.4142135623731	(π/4, 1.4142135623731)
π/6	sec([π/6])	1.1547005383793	(π/6, 1.1547005383793)

Determine the y-intercept:

The y-intercept is found when x is set to 0. From the grid above, our y-intercept is 1.1547005383793

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 (-∞, 1) U (1, ∞)

(2π, 1)
(11π/6, 1.1547005383793)
(7i/4, 1.4142135623731)
(5π/3, 2)
(3π/2, -5.4437464510651E+15)
(4π/3, -2)
(5π/4, -1.4142135623731)
(7π/6, -1.1547005383793)
(π, -1)
(5π/6, -1.1547005383793)
(3π/4, -1.4142135623731)
(2π/3, -2)
(π/2, 1.6331239353195E+16)
(π/3, 2)
(π/4, 1.4142135623731)
(π/6, 1.1547005383793)

What is the Answer?

How does the Function Calculator work?

Free Function Calculator - 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?

The y-intercept is found when x is set to 0
The x-intercept is found when y is set to 0
The domain represents all values of x that you can enter
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?

domainSet of all possible input values which makes the output value of a function validfunctionrelation between a set of inputs and permissible outputs
ƒ(x)ordered pairA pair of numbers signifying the location of a point
(x, y)rangeDifference between the largest and smallest values in a number set

sec(x)