Question

Based on the family the graph below belongs to, which equation could represent the graph?

Answer 1

Considering the asymptotes of the function, the equation that represents the graph is:

$y = \frac{1}{x + 2} + 3$

What are the asymptotes of a function f(x)?

• The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

• The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

This function, from the graph, has a vertical asymptote at x = -2, hence the denominator is given by:$y = \frac{1}{x + 2} + 3$

x + 2, as x + 2 = 0 -> x = -2.

The horizontal asymptote is of y = 3, hence:

$\lim_{x \rightarrow \infty} f(x) = 3$

Which means that the function is described by the following rule:

$y = \frac{1}{x + 2} + 3$

More can be learned about asymptotes at https://brainly.com/question/16948935

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