Shown below
Explanation:
[tex]f(x) = \frac{2}{x^2+5}[/tex]
Let's analyze this function. In order for this function to be continuous, the denominator can't be zero. So:
[tex]x^2+5 \neq 0[/tex]
But this is never zero because [tex]x^2[/tex] gives us a positive number that added to 5 also gives us a positive number. Therefore this function is continuous from [tex]-\infty \ to \ \infty[/tex].
When x tends to [tex]-\infty \ to \ \infty[/tex] the graph of the function approaches zero and when [tex]x=0[/tex] then [tex]y=0.4[/tex]
So we get the graph shown below.
