Question

Need help with rational function question for precalculus

Answer 1

Answers: 1), 2), 3).

Explanation:

Note that when we say
`x \to a^-`, we mean "as x tends to a from the left hand side". That is, what is the function doing when "x approaches a from the left side". In much the same way, we say
`x \to a^+` to imply what the function is doing when "x approaches from the right side".

So, when
`x \to 3^-`, we are looking at the point around x = 3, but from the left side. From the graph, we see that, from the left side of 3, the graph is approaching a fairly big number. So, we see that: "As
`x \to 3^-`,
`f(x) \to \infty`".

In much the same way:

"As
`x \to 3^+`,
`f(x) \to -\infty`".

"As
`x \to \infty`,
`f(x) \to 2`".