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Chapter 3: Problem 44

Find the horizontal asymptote, if there is one, of the graph of each rational function. $$ f(x)=\frac{-3 x+7}{5 x-2} $$

Short Answer

Expert verified
The horizontal asymptote of the function \(f(x) = \frac{-3x + 7}{5x - 2}\) is \(y = -3/5\).

Step by step solution

01

Identifying the Coefficients of the Highest Power of x in the Numerator and Denominator

Look at the coefficients of the x terms in the numerator and denominator. In our function, the coefficient in the numerator is -3 (from -3x) and in the denominator is 5 (from 5x).
02

Calculating the Ratio of the Coefficients

Calculate the ratio of the coefficient in the numerator to the coefficient in the denominator. In this case, the ratio is \(-3/5\)
03

Identify the Horizontal Asymptote

The ratio obtained in step 2 gives the equation of the horizontal asymptote. Therefore, the line \(y = -3/5\) is the horizontal asymptote.

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