Does the graph of the function f(x) = x^2 − 8x − 9 / x + 1 have a vertical asymptote or a point missing at x = −1? explain
your reasoning, and support your answer numerically.

Yes, the graph of the function has vertical asymptote at x=-1.

Step-by-step explanation:

Given : Function

To find : Does the graph of the function have a vertical asymptote or a point missing at x = −1?

Solution :

The vertical asymptote of the rational function is when we put denominator equals to zero.

In the function

Denominator -

Vertical asymptote is at

Yes, the graph of the function has vertical asymptote at x=-1.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form