PRACTICE QUESTIONS ON FINDING HORIZONTAL AND VERTICAL ASYMPTOTES

Find the vertical and horizontal asymptotes of the function given below.

(1) f(x) = -4/(x² - 3x) Solution

(2) f(x) = (x-4)/(-4x-16) Solution

(3) f(x) = (x+4)/(-2x-6) Solution

(4) f(x) = (x³-9x)/(3x²-6x-9) Solution

(5) f(x) = (3x²-12x)/(x²-2x-3) Solution

(6) f(x) = (x³-16x)/(-4x²+4x+24) Solution

(7) f(x) = (x²+2x)/(-4x+8) Solution

(8) f(x) = 4x²/(x²+ 8) Solution

(9) f(x) = (4x+5)/(4x²-9) Solution

(10) f(x) = (x³+2x+1)/(x²-x-12) Solution

(11) f(x) = (4x²-3)/(2x²-3x+1) Solution

(12) f(x) = ln(2x+3) Solution

Vertical Asymptotes

(1) x = 0 and x = 3

(2) x = -4

(3) x = -3

(4) x = 3 and x = -1.

(5) x = 3 and x = -1.

(6) x = 3 and x = -2

(7) x = 2

(8) No VA

(9) x = 3/2 and x = -3/2.

(10) x = 4 and x = -3.

(11) x = 1/2 and x = 1.

(12) x = -3/2

Horizontal asymptotes

y = 0

y = -1/4

y = -1/2

no HA

y = 3

no HA

y = 4

y = 0.

No HA

y = 2

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