Rational Functions Calculator

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Example

Created on 2024-06-20Asked by William Harris (Solvelet student)

Find the vertical asymptotes of the rational function:

f(x) = \frac{2x}{x^2 - 4}.

Solution

To find the vertical asymptotes of the rational function

f(x) = \frac{2x}{x^2 - 4}

: 1. **Factor the denominator:**

x^2 - 4 = (x - 2)(x + 2).

2. **Set the denominator equal to zero to find the vertical asymptotes:**

x - 2 = 0 \quad \Rightarrow \quad x = 2,

x + 2 = 0 \quad \Rightarrow \quad x = -2.

Therefore, the vertical asymptotes of the function are

x = 2

and

x = -2

. Solved on Solvelet with Basic AI Model

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1. Identify the vertical and horizontal asymptotes of the function

f(x) = \frac{x^2 - 9}{x - 3}

.2. Find the equation of the oblique asymptote of the function

f(x) = \frac{2x^2 + 3x - 5}{x + 1}

DefinitionRational functions are the ratios of two polynomials. Written in the form f(x)=Q(x)P(x), P(x) and Q(x) are polynomials and Q(x)=0. Example:The function f(x)=x2−12x+3 is a rational function.

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