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Home » Map It & Dominate: ZIP Code Reveals the Secret to Top-Rated Homes in Charlotte! - ClickBalance

Map It & Dominate: ZIP Code Reveals the Secret to Top-Rated Homes in Charlotte! - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Find the horizontal asymptote of this function as \( t \to \infty \).

📌 To find the horizontal asymptote of the rational function \( G(t) = \frac{3t^2 + 2t + 1}{t + 1} \), we analyze the degrees of the numerator and the denominator.

📌 The degree of the numerator is 2, and the degree of the denominator is 1. Since the degree of the numerator is greater than the degree of the denominator, the function does not have a horizontal asymptote. Instead, it has an oblique (slant) asymptote.

📌 To find the slant asymptote, perform polynomial long division of \( 3t^2 + 2t + 1 \) by \( t + 1 \):

📌 Divide \( 3t^2 \) by \( t \) to get \( 3t \).

📌 Multiply \( 3t \) by \( t + 1 \): \( 3t^2 + 3t \).

📌 Subtract: \( (3t^2 + 2t + 1) - (3t^2 + 3t) = -t + 1 \).

📌 Divide \( -t \) by \( t \) to get \(-1\).

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