y= 1/x-3 - Wolfram|Alpha

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Input

y = 1/x - 3

Geometric figure

hyperbola

Plot

Plot

Plot

Alternate form

y + 3 = 1/x

y = -(3 x - 1)/x

Alternate form assuming x and y are positive

x (y + 3) = 1 (for x!=0)

Root

x = 1/3

Properties as a real function

Domain

{x element R : x!=0}

Range

{y element R : y!=-3}

Injectivity

injective (one-to-one)

Partial derivatives

d/dx(1/x - 3) = -1/x^2

d/dy(1/x - 3) = 0

Implicit derivatives

(dx(y))/(dy) = -x^2

(dy(x))/(dx) = -1/x^2

Limit

lim_(x-> ± ∞)(-3 + 1/x) = -3

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