Question Find the equation of all horizontal asymptotes of the following function. f(x)=-(9)/(4x+24)+1

To find the horizontal asymptotes of the function \( f(x) = -\frac{9}{4x+24} + 1 \), we need to analyze the behavior of the function as \( x \) approaches positive and negative infinity.<br /><br />First, let's rewrite the function in a more convenient form:<br />\[ f(x) = -\frac{9}{4x+24} + 1 \]<br /><br />As \( x \) approaches positive or negative infinity, the term \(\frac{9}{4x+24}\) approaches 0 because the denominator grows without bound. Therefore, the function simplifies to:<br />\[ \lim_{x \to \pm\infty} f(x) = -\frac{9}{4x+24} + 1 \approx 1 \]<br /><br />Thus, the horizontal asymptote of the function is:<br />\[ y = 1 \]<br /><br />So, the equation of the horizontal asymptote is:<br />\[ y = 1 \]