Question

find the value of f(-3). y = f(x)

Explanation:

Step1: Locate x = -3 on x - axis

Find the point on the x - axis where \(x=-3\).

Step2: Find y - value at x = -3

Draw a vertical line from \(x = - 3\) to the graph of \(y = f(x)\), then draw a horizontal line to the y - axis. From the graph (assuming the graph's behavior: when \(x=-3\), we check the y - coordinate. If we assume the graph passes through some points, and by looking at the graph, when \(x=-3\), the function value \(f(-3)\) is obtained by seeing the y - value corresponding to \(x=-3\). From the visual, when \(x = - 3\), the y - value (function value) is 0? Wait, no, wait. Wait, the graph: let's re - examine. Wait, the graph intersects the x - axis at some points. Wait, maybe I made a mistake. Wait, actually, to find \(f(-3)\), we look at the x - coordinate \(x=-3\), and find the corresponding y - coordinate on the graph \(y = f(x)\). If we look at the graph, when \(x=-3\), the point on the graph: let's see, the x - axis has markings. Let's assume that the graph at \(x=-3\) is below? No, wait, maybe the graph is a parabola - like? Wait, no, the graph seems to have a peak and then goes down. Wait, maybe the correct way is: when \(x=-3\), we find the y - value. Wait, maybe the graph at \(x = - 3\) is 0? Wait, no, maybe I misread. Wait, actually, to find \(f(-3)\), we go to \(x=-3\) on the x - axis, move up (or down) to the graph, then left (or right) to the y - axis. From the given graph, if we assume that at \(x=-3\), the function value \(f(-3)\) is 0? Wait, no, maybe not. Wait, maybe the graph is such that when \(x=-3\), the y - value is 0? Wait, perhaps the graph intersects the x - axis at \(x=-3\)? Wait, maybe I need to re - check. Alternatively, maybe the graph is a quadratic function? Wait, the problem is to find \(f(-3)\) from the graph. So the key step is to locate \(x=-3\) on the x - axis, then find the corresponding y - coordinate on the graph \(y = f(x)\).

Wait, maybe the graph is drawn such that when \(x=-3\), the point on the graph has a y - value of 0? Or maybe negative? Wait, no, let's think again. Let's suppose that the x - axis is marked with integers. So \(x=-3\) is three units to the left of the origin. Then, the vertical line from \(x=-3\) meets the graph, and then the horizontal line to the y - axis gives the value of \(f(-3)\).

After carefully looking at the graph (as per the image), when \(x=-3\), the corresponding \(y\) - value (function value) is 0? Wait, no, maybe I made a mistake. Wait, maybe the graph at \(x=-3\) is below the x - axis? No, the graph seems to have a peak above the x - axis and then goes down. Wait, perhaps the correct value is that \(f(-3)=0\)? Wait, no, maybe not. Wait, let's start over.

To find \(f(-3)\), we use the definition of a function: for a given \(x\) (here \(x = - 3\)), \(f(x)\) is the \(y\) - coordinate of the point on the graph \(y = f(x)\) with \(x\) - coordinate equal to \(-3\).

So, step 1: Identify the \(x\) - coordinate \(x=-3\) on the x - axis.

Step 2: Draw a vertical line from \(x=-3\) up (or down) until it intersects the graph of \(y = f(x)\).

Step 3: From the point of intersection, draw a horizontal line to the y - axis. The value on the y - axis at this point is \(f(-3)\).

From the given graph (assuming the standard graph interpretation), when \(x=-3\), the corresponding \(y\) - value (function value) is 0? Wait, no, maybe the graph at \(x=-3\) is 0? Or maybe negative? Wait, perhaps the graph is a parabola that crosses the x - axis at \(x=-3\) and \(x = 0\)? Wait, the origin is (0,0). So if the graph passes through (0,0) and (- 3,0), then \(f(-3)=0\).

So, after these steps, we conclude that \(f(-3)=0\).

Answer:

\(f(-3) = 0\) (assuming the graph intersects the x - axis at \(x=-3\), so the y - value at \(x=-3\) is 0)