Answer
a) See table
b) See graph
c) $y=-6,y=6$
Work Step by Step
We are given the function:
$f(x)=\dfrac{12x+1}{\sqrt{4x^2+9}}$
a) Compute the values of $f$ for $x=\pm 100,\pm 500,\pm 1000,\pm 10,000$:
b) Plot the graph of $f$:
c) Determine the horizontal asymptotes of $f$:
$\displaystyle\lim_{x\rightarrow -\infty} f(x)=-6\Rightarrow y=-6$
$\displaystyle\lim_{x\rightarrow \infty} f(x)=-6\Rightarrow y=6$
