which function is represented by the graph?\n○ (f(x)=-2|x| + 1)\n○ (f(x)=-\frac{1}{2}|x| + 1)\n○ (f(x)=-2|x…

which function is represented by the graph?\n○ (f(x)=-2|x| + 1)\n○ (f(x)=-\frac{1}{2}|x| + 1)\n○ (f(x)=-2|x + 1|)\n○ (f(x)=-\frac{1}{2}|x + 1|)

which function is represented by the graph?\n○ (f(x)=-2|x| + 1)\n○ (f(x)=-\frac{1}{2}|x| + 1)\n○ (f(x)=-2|x + 1|)\n○ (f(x)=-\frac{1}{2}|x + 1|)

Answer

Answer:

B. $f(x)=-\frac{1}{2}|x| + 1$

Explanation:

Step1: Identify vertex

The vertex of the graph is at $(0,1)$. For absolute - value functions of the form $y = a|x - h|+k$, the vertex is $(h,k)$. Here $h = 0,k = 1$, so we can rule out options C and D since they have $h=-1$.

Step2: Determine the slope

Take a non - vertex point, say $(2,0)$. Substitute $x = 2$ and $y = 0$ into the remaining options. For $y=-2|x| + 1$, when $x = 2$, $y=-2\times|2|+1=-4 + 1=-3\neq0$. For $y=-\frac{1}{2}|x|+1$, when $x = 2$, $y=-\frac{1}{2}\times|2|+1=-1 + 1=0$. So the function is $f(x)=-\frac{1}{2}|x| + 1$.