Stationary Points and Asymptotes of Rational Function
1300ApprenticeCalculusFunctions
19. tekmovanje v znanju matematike za dijake srednjih tehniških in strokovnih šol Državno tekmovanje
Two real functions are given: $f(x)=x+1$ and $g(x)=x^{2}+3$.
a) The function $h$ is defined by $h(x)=\frac{f(x)+g(x)}{g(x)}$. Find the stationary points of the function $h$. Write the equation of the horizontal asymptote of the graph of $h$ and compute the intersection point of the graph with the horizontal asymptote.
b) Determine for which $a \in \mathbb{R}$ the function $j(x)=g(x)+a f(x)-a$ has at least one real zero.