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

$1398_w220_h41.png$

Question:

$1398_w220_h41.png$

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

Range: $4246_w59_h37.png$, $8657_w44_h37.png$, 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: $4246_w59_h37.png$, $8657_w44_h37.png$, y \u2260 0

Horizontal Asymptote: y = 0

Vertical Asymptote: x = -1

Explaination

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

$3043_w230_h43.png$

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: $1890_w103_h39.png$. So:

$7670_w136_h39.png$

and

$5004_w179_h39.png$

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

$4314_w136_h39.png$, which gives

$1992_w78_h41.png$, so y \u2260 0

From the reduced function: $1546_w103_h39.png$, 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: $2885_w176_h43.png$, giving the point (0, 1)

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