Question

Which of the following functions will produce the graph shown below?

Answer 1

The answer is B.

`y = \frac{ {x}^(2) - 1}{ {x}^(2) + 2x - 3 }`

Step-by-step explanation

The graph represents a rational function.

This rational function has a hole at x=1 and a vertical asymptote at x=-3.

This implies that the denominator of the rational function in factored form is

`(x + 3)(x - 1)`

When we expand this, we get:

`{x}^(2) + 2x - 3`

This tells us that the answer must be option B.

This graph also has a horizontal asymptote at y=1.

The numerator must therefore have leading term that is quadratic with the coefficient being unity or 1.

Therefore the function is actually

`y = \frac{ {x}^(2) - 1}{ {x}^(2) + 2x - 3 }`