Question

evaluate the function graphically.
find f(-5)

Explanation:

Step1: Locate x = -5 on x - axis

Find the point on the x - axis where \(x=-5\).

Step2: Find corresponding y - value

From the graph, the curve (the quadratic - like part) passes through \(x = - 5\). We look at the y - coordinate of the point on the graph when \(x=-5\). By observing the graph, when \(x=-5\), the point on the curve has a y - value of \(0\)? Wait, no, let's re - examine. Wait, the left - hand curve: when \(x=-5\), let's check the graph. Wait, the curve is a parabola - like shape. Let's see the x - intercepts: the curve crosses the x - axis at \(x=-5\) and another point? Wait, no, when \(x = - 5\), we move up (or down) from \(x=-5\) on the x - axis to the graph. Wait, actually, when \(x=-5\), the point on the graph (the left curve) has a y - value of \(0\)? Wait, no, let's check again. Wait, the graph: the left curve, when \(x=-5\), we can see that the curve passes through \((-5,0)\)? Wait, no, maybe I made a mistake. Wait, let's look at the graph structure. The left part is a parabola - shaped curve. Let's find the value of \(f(-5)\). To find \(f(-5)\), we find the y - coordinate of the point on the graph where \(x = - 5\). From the graph, when \(x=-5\), the point on the curve (the left - hand function) has a y - value of \(0\)? Wait, no, maybe I misread. Wait, let's check the x - axis: \(x=-5\) is on the x - axis. The curve (the quadratic part) passes through \(x=-5\), so the y - value at \(x=-5\) is \(0\)? Wait, no, let's see the graph again. Wait, the left curve: when \(x=-5\), moving vertically to the curve, the y - coordinate is \(0\)? Wait, maybe. Wait, actually, when we look at the graph, the left - hand function (the parabola - like) at \(x=-5\) has a y - value of \(0\)? Wait, no, let's check the coordinates. Wait, the x - axis is marked with - 10, - 9, ..., - 5, - 4, etc. The curve crosses the x - axis at \(x=-5\) (since it's on the x - axis, y = 0) and maybe another point. So when \(x=-5\), \(f(-5)=0\)? Wait, no, wait, maybe I made a mistake. Wait, let's re - analyze. The graph: the left part is a curve that goes from down, up to a peak, then down. At \(x=-5\), the curve is on the x - axis, so \(y = 0\). So \(f(-5)=0\)? Wait, no, wait, when \(x=-5\), the point on the graph (the left curve) has \(y = 0\). So the value of \(f(-5)\) is \(0\)? Wait, maybe. Let's confirm: to evaluate \(f(-5)\) graphically, we find the point with \(x=-5\) on the graph and read its y - coordinate. From the graph, the curve (the left - hand function) at \(x=-5\) has a y - value of \(0\).

Answer:

\(0\)