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3 years ago

5

Identify the oblique asymptote of f(x) = quantity x plus 4 over quantity 3 x squared plus 5 x minus 2.

2 answers:

aliya0001 [1]3 years ago

8 0

Answer is no oblique asymptotes

faltersainse [42]3 years ago

3 0

$f(x) = \frac{x + 4}{3x^{2} + 5x - 2}$

3x² + 5x - 2 = 0
  3x² + 6x - x - 2 = 0
3x(x) + 3x(2) - 1(x) - 1(2) = 0
  3x(x + 2) - 1(x + 2) = 0
(3x - 1)(x + 2) = 0
3x - 1 = 0     or       x + 2 = 0
+ 1 + 1 - 2 - 2
3x = 1 or x = -2
3 3   1 1
x = ¹/₃ or x = -2

  f(x) = 3x² + 5x - 2
f(¹/₃) = 3(¹/₃)² + 5(¹/₃) - 2
f(¹/₃) = 3(¹/₉) + 1²/₃ - 2
f(¹/₃) = ¹/₃ - ¹/₃
f(¹/₃) = 0
(x, f(x)) = (¹/₃, 0)

f(x) = 3x² + 5x - 2
f(-2) = 3(-2)² + 5(-2) - 2
f(-2) = 3(4) - 10 - 2
f(-2) = 12 - 12
f(-2) = 0
(x, f(x)) = (-2, 0)

  Vertical Asymptotes: ¹/₃ or -2
Horizontal Asymptotes: 0
  Oblique Asymptote: No Asymptotes

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