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 $a=-2<0$. For absolute value functions with $a<0$, 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: Evaluate limit at $+\infty$

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

Answer:

1. maximum
2. decreasing
3. negative