Question

1. write the equation of the function f(x) shown in the graph. f(x) = ____________

Explanation:

Step1: Identify the function type

The graph is a V - shaped graph, which is the graph of an absolute - value function of the form $y = a|x - h|+k$, where $(h,k)$ is the vertex of the V - shaped graph.

Step2: Determine the vertex

The vertex of the given graph is at the point $(0, - 3)$. So, $h = 0$ and $k=-3$.

Step3: Determine the value of a

Since the slope of the right - hand side of the graph (for $x\geq0$) is 1 (we can see that for every 1 unit increase in $x$, there is a 1 unit increase in $y$), and for the absolute - value function $y = a|x - h|+k$, the slope of the right - hand side is $a$ when $x\geq h$. Here $a = 1$.

Step4: Write the function

Substitute $a = 1$, $h = 0$, and $k=-3$ into the formula $y = a|x - h|+k$. We get $f(x)=|x|-3$.

Answer:

$f(x)=|x|-3$