Based on the family the graph below belongs to, which equation could represent the graph? On a coordinate plane, 2 curves are shown. One curve approaches x = negative 2 in quadrant 2 and then decreases into quadrant 1. It crosses the y-axis at (0, 3.5). Another curve approaches x = negative 2 in quadrant 3 and then increases into quadrant 2. It crosses the x-axis at (negative 2.5, 0). y = StartFraction 1 Over x + 2 EndFraction + 3 y = 0.2 Superscript x Baseline + 3 y = x cubed + 3 y = log x + 3

a. y = 1/(x + 2) + 3

Step-by-step explanation:

From the description of the function, it is seen that the curve has an asymptote at x = -2. Asymptotes are typical from rational functions. The only option that matches this feature is y = 1/(x + 2) + 3

Moreover, replacing x = 0 into the equation, we get:

y = 1/(0 + 2) + 3 = 3.5

And replacing y = 0 into the equation, we get:

0 = 1/(x + 2) + 3

-3 = 1/(x + 2)

x + 2 = -1/3

x = -1/3 - 2

x = -2.33 ≈ -2.5

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