Question

what is the equation of the absolute value function? f(x)= |x+4| f(x)= |x| + 4 f(x)= |x| - 4 f(x)= |x-4|

Explanation:

Step1: Recall absolute value function form

The general form of an absolute value function is \( f(x) = |x - h| + k \), where \((h, k)\) is the vertex. From the graph, the vertex is at \((0, 4)\) (since it's on the y - axis at \(y = 4\)).

Step2: Substitute h and k into the form

Here, \(h = 0\) and \(k = 4\). Substituting into \(f(x)=|x - h|+k\), we get \(f(x)=|x - 0|+4=|x| + 4\). We can also check by plugging in \(x = 0\): for \(f(x)=|x| + 4\), \(f(0)=|0|+4 = 4\), which matches the vertex's y - coordinate. For \(f(x)=|x + 4|\), \(f(0)=|4| = 4\) (wait, no, \(|0 + 4|=4\), but the vertex of \(y = |x + 4|\) is at \((-4,0)\), which doesn't match. For \(f(x)=|x|-4\), \(f(0)=-4\), wrong. For \(f(x)=|x - 4|\), \(f(0)=| - 4|=4\), but vertex is at \((4,0)\), wrong. So the correct one is \(f(x)=|x| + 4\).

Answer:

B. \(f(x)=|x| + 4\)