Question

select the correct answer from each drop - down menu. complete the statements about this function: $f(x)=-2|x + 1|+2$. the vertex of the function is a drop - down menu. on the interval $(-1,\infty)$, the function is drop - down menu. as $x$ approaches positive infinity, the function approaches drop - down menu infinity.

Explanation:

Step1: Identify vertex type

The function is in the form $f(x)=a|x-h|+k$, where $a=-2<0$. A negative leading coefficient means the absolute value graph opens downward, so the vertex is a maximum.

Step2: Analyze interval behavior

For $x > -1$, $|x+1|=x+1$, so $f(x)=-2(x+1)+2=-2x$. The slope is $-2<0$, so the function decreases on $(-1,\infty)$.

Step3: Find limit as $x\to\infty$

As $x\to+\infty$, $|x+1|\to+\infty$, so $f(x)=-2|x+1|+2\to-\infty$.

Answer:

1. The vertex of the function is a maximum
2. On the interval $(-1, \infty)$, the function is decreasing
3. As $x$ approaches positive infinity, the function approaches negative infinity.