What is the horizontal asymptote of the equation y = (x + 3)/(x^2 + 3x - 4)?

What is the horizontal asymptote of the equation y = (x + 3)/(x^2 + 3x - 4)?

• A. y = 1
• B. y = 0
• C. y = 3
• D. y = -1

Answer: (B)

To determine the horizontal asymptote of the function y = (x + 3)/(x^2 + 3x - 4), it is important to analyze the degrees of the polynomial in the numerator and the polynomial in the denominator. In this equation, the numerator, (x + 3), is a first-degree polynomial (since it has the highest power of x being 1). The denominator, (x^2 + 3x - 4), is a second-degree polynomial (because the highest power of x is 2). When the degree of the polynomial in the numerator is less than the degree of the polynomial in the denominator, the horizontal asymptote is found at y = 0. This indicates that as x approaches positive or negative infinity, the values of y will approach 0. Therefore, for the given function, as the value of x becomes very large or very small, the influence of the higher degree term in the denominator dominates, leading the overall function towards zero. This analysis confirms that the horizontal asymptote of the function is indeed y = 0.

To determine the horizontal asymptote of the function y = (x + 3)/(x^2 + 3x - 4), it is important to analyze the degrees of the polynomial in the numerator and the polynomial in the denominator.

In this equation, the numerator, (x + 3), is a first-degree polynomial (since it has the highest power of x being 1). The denominator, (x^2 + 3x - 4), is a second-degree polynomial (because the highest power of x is 2).

When the degree of the polynomial in the numerator is less than the degree of the polynomial in the denominator, the horizontal asymptote is found at y = 0. This indicates that as x approaches positive or negative infinity, the values of y will approach 0.

Therefore, for the given function, as the value of x becomes very large or very small, the influence of the higher degree term in the denominator dominates, leading the overall function towards zero.

This analysis confirms that the horizontal asymptote of the function is indeed y = 0.