- 1). Write the function, or equation, you want to analyze. For example, you write, y = (5x^3 + 3)/(2x^3 - 7).
- 2). Identify the largest exponent of x in the numerator of the function. Write this exponent as N. An exponent is a superscript number immediately following a letter variable. For example, the exponent after x in the numerator of the function you have written is 3. You write, "N = 3."
- 3). Identify the largest exponent following x in the denominator of the function. Write this exponent as D. For example, the exponent after x in the denominator of the function you have written is 3. You write, "D = 3."
- 4). Find the quotient of N and D using a calculator. For example, N/D = 3/3 = 1.
- 5). Note that if the quotient of N and D equals 1, the function has a horizontal asymptote.
- 6). Identify the coefficients of the x values you have analyzed in the numerator and denominator. A coefficient is a number immediately preceding a letter variable. For example, the coefficient of x in the numerator of your function is 5 and the coefficient of x in the denominator of your function is 2.
- 7). Find the quotient of the numerator coefficient and the denominator coefficient using a calculator. For example, 5/2 = 2.5.
- 8). Note that the horizontal asymptote of the function, or equation, you have written is at y = 2.5.
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