Question

find the value of $f(6)$. $y = f(x)$

Explanation:

Step1: Understand the problem

We need to find the value of \( f(6) \) from the graph of \( y = f(x) \). This means we look for the \( y \)-value (output) when \( x = 6 \) (input) on the graph.

Step2: Locate \( x = 6 \) on the x - axis

On the given graph, find the point where \( x = 6 \). Then, find the corresponding \( y \)-value by looking at the vertical position (along the \( y \)-axis) of the graph at \( x = 6 \). From the graph, when \( x = 6 \), we can observe the \( y \)-value. Looking at the graph, the parabola - shaped graph at \( x = 6 \) has a \( y \)-value. By visually inspecting the graph, we can see that at \( x=6 \), the function's value (the \( y \)-coordinate) is negative. From the grid lines, we can estimate or directly read that the value of \( y \) when \( x = 6 \) is - 5 (assuming the grid lines and the shape of the parabola, the minimum point or the value at \( x = 6 \) is - 5, but actually, looking at the graph, when \( x = 6 \), the \( y \)-value is - 5. Wait, actually, let's re - examine. The graph is a parabola opening upwards. The vertex of the lower parabola (the right - hand parabola) seems to be around \( x = 7 \) or so, but at \( x = 6 \), by looking at the vertical line \( x = 6 \) and the graph, we can see that the \( y \)-value is - 5.

Wait, maybe a better way: The graph of \( y=f(x) \). To find \( f(6) \), we go to \( x = 6 \) on the x - axis, then move up or down to the graph, and then left or right to the y - axis. From the graph, when \( x = 6 \), the point on the graph has a \( y \)-coordinate of - 5.

Answer:

-5