Question

input output -2 -4 2 4

Explanation:

Step1: Analyze the graph's symmetry

The graph appears to be symmetric about the y - axis (since the left and right sides of the y - axis mirror each other). For a function with y - axis symmetry, \(f(x)=f(-x)\).

Step2: Use the given input - output and symmetry

We know that when \(x = - 2\), the output (function value) is \(-4\). Since the graph is symmetric about the y - axis, for \(x = 2\) (which is the opposite of \(x=-2\) with respect to the y - axis), the function value should be the same as when \(x=-2\). So when \(x = 2\), the output is \(-4\).

Step3: Analyze the point at \(x = 4\)

Looking at the graph, we can see that the point at \(x = 4\) is at the minimum of the right - hand "valley" of the graph. From the graph, we can observe that the y - coordinate (output) at \(x = 4\) is \(-6\) (by looking at the grid lines, the point is at \(y=-6\)).

Answer:

For \(x = 2\), the output is \(-4\); for \(x = 4\), the output is \(-6\)