Question

evaluate the function graphically.
find ( f(7) )

Explanation:

Step1: Identify the function's equation

First, we find the slope of the line. The line passes through \((0, -1)\) and, for example, when \(x = -5\), the open circle is at \(y = 4\)? Wait, no, let's check the intercept. Wait, the line crosses the y-axis at \((0, -1)\), and let's find another point. Wait, when \(x = -5\), the open circle is at \(y = 4\)? Wait, no, the line: let's take two points. Let's see, the line goes through \((0, -1)\) and let's find the slope. Wait, when \(x = 7\), we need to find \(f(7)\). Let's find the equation of the line. The slope \(m\): let's take two points on the line. Let's see, when \(x = -5\), the open circle is at \(y = 4\), but the solid line? Wait, no, the line is a straight line. Let's check the y-intercept: at \(x = 0\), \(y = -1\). Let's take another point. When \(x = 1\), what's \(y\)? Let's see the grid. Wait, the line has a slope. Let's calculate the slope between \((0, -1)\) and, say, \((-5, 4)\) (the open circle, but is that on the line? Wait, the line is the straight line, so the equation of the line: let's use two points. Let's take \((0, -1)\) and, for example, when \(x = 1\), \(y = -2\)? Wait, no, let's do it properly. The slope \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let's take \((0, -1)\) and \((1, -2)\): \(m = \frac{-2 - (-1)}{1 - 0} = \frac{-1}{1} = -1\). So the equation is \(y = -x - 1\).

Step2: Substitute \(x = 7\) into the equation

Now, to find \(f(7)\), we substitute \(x = 7\) into \(y = -x - 1\). So \(y = -7 - 1 = -8\). Wait, but let's check the graph. The line extends to \(x = 7\), so we can use the equation. Alternatively, since the line has a slope of -1 and y-intercept -1, the equation is \(y = -x - 1\). So when \(x = 7\), \(y = -7 - 1 = -8\).

Answer:

\(-8\)