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1212Which answer choice best provides the critical information regarding the following rational function:

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Question:

A
1212Domain: x \u2260 -1, x \u2260 -3, x \u2260 2

Range: , , y \u2260 0

Horizontal Asymptote: y = 0

Vertical Asymptote: x = -1

*y*-intercept: (0, 1) End Behavior: f(x) approaches negative infinity as *x* approaches -1 from the left. f(x) approaches positive infinity as *x* approaches -1 from the right.

Range: , , y \u2260 0

Horizontal Asymptote: y = 0

Vertical Asymptote: x = -1

explanation

1212Begin by factoring the first expression and rewriting the division as an inverse multiplication:

The function shows a discontinuity at x = 2 and x = -3. It shows a vertical asymptote at x = -1.

To find the excluded range values corresponding to the discontinuities, substitute the *x* values into the reduced function: . So:

and

Solving the function for *x* enables another excluded range value to be found:

, which gives

, so y \u2260 0

From the reduced function: , it can be seen that as *x* increases, f(x) approaches 0, and that as *x* approaches -1 from the right, f(x) approaches infinity. As *x* decreases, f(x) approaches 0, and as *x* approaches -1 from the left, f(x) approaches negative infinity.

Lastly, the *y* intercept: , giving the point (0, 1)

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