Learn Math Questions

from a handpicked tutor in LIVE 1-to-1 classes

from a handpicked tutor in LIVE 1-to-1 classes

# What are the vertical and horizontal asymptotes for the function f(x) = 3x^{2}/x^{2 }- 4

**Solution:**

Horizontal __asymptotes__ are nothing but the lines parallel to __x - axis__ which exists when fꞌ(x) = 0

And vertical asymptotes are nothing but the lines parallel to __y - axis__ which exists when fꞌ(x) = Not defined.

Consider f(x)=3x^{2}/x^{2 }- 4

__Differentiate__ w.r.to x

fꞌ(x) = {(x^{2 }- 4) (6x ) - 3x^{2 }(2x)}/ (x^{2 }- 4)²

Now for fꞌ(x) = 0

⇒ (x^{2 }- 4) (6x ) - 3x^{2 }(2x) = 0

⇒ 2x { 3x^{2 } - 12x - 3x^{2 } } = 0

⇒ x = 0

∴ Horizontal asymptotes is x = 0 ⇒ y = 0 which is x - axis

Now for fꞌ(x) =∞

⇒(x^{2 }- 4)² = 0

⇒ x^{2 }= 4

⇒ x = ± 2

∴ Vertical asymptotes are x = 2 and x = -2

## What are the vertical and horizontal asymptotes for the function f(x) = 3x^{2}/x^{2 }- 4

**Summary:**

Horizontal asymptotes is x = 0 ⇒ y = 0 which is x - axis, Vertical asymptotes are x = 2 and x = -2.

Math worksheets and

visual curriculum

visual curriculum