Question

1. Use the graph of the rational function

to complete the following statement.
As x → -3*, f(x) →
N

Answer 1

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

Explanation:

Given:

From the graph, we can conclude that:

The function has vertical asymptotes at
`x=-3\ and\ x=2`

The function has horizontal asymptote at
`f(x)=0`

Vertical asymptotes are those values of 'x' for which the functions tends towards infinity. Horizontal asymptote is the value of the function as the 'x' value tends to infinity.

Now, as
`x \to -3^(+)` means the right hand limit of the function at
`x=-3`

From the graph, the right hand limit is the right side of the asymptote of the function at
`x = -3`. The right side shows that the function is tending towards negative infinity.

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