 Question:

# Which answer choice best provides the critical information regarding the following rational function: \$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.
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)