Question

problem
$y = \frac{2 - x}{x + 2}$
x - intercept:
2
vertical asymptote:
$x = -2$
leading term:
-1
horizontal asymptote:
$y = -1$
pattern of signs:
enter text more...
e.g., +++--, no commas.
degree:
1
degree:
1

Explanation:

Step1: Identify critical points

Critical points are $x=-2$ (vertical asymptote) and $x=2$ (x-intercept). These divide the number line into 3 intervals: $(-\infty,-2)$, $(-2,2)$, $(2,+\infty)$.

Step2: Test sign in $(-\infty,-2)$

Choose $x=-3$, substitute into $y=\frac{2-x}{x+2}$:
$y=\frac{2-(-3)}{-3+2}=\frac{5}{-1}=-5$, sign is $-$.

Step3: Test sign in $(-2,2)$

Choose $x=0$, substitute into $y=\frac{2-x}{x+2}$:
$y=\frac{2-0}{0+2}=1$, sign is $+$.

Step4: Test sign in $(2,+\infty)$

Choose $x=3$, substitute into $y=\frac{2-x}{x+2}$:
$y=\frac{2-3}{3+2}=\frac{-1}{5}=-0.2$, sign is $-$.

Answer:

$- + -$