Question

find the value of $f(-4)$.
$y = f(x)$
(graph of a piecewise linear function with a line passing through the grid, x-axis from -10 to 10, y-axis from -10 to 10)
answer
attempt 1 out of 2
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Explanation:

Step1: Determine the equation of the line

The line passes through the points \((0, 1)\) and \((-1, 0)\) (we can also use other points, but these are easy to identify). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 1}{-1 - 0}=1\). Using the slope - intercept form \(y = mx + b\), with \(m = 1\) and \(b = 1\) (since the y - intercept is at \((0,1)\)), the equation of the line is \(y=x + 1\).

Step2: Substitute \(x=-4\) into the equation

We want to find \(f(-4)\), and since \(y = f(x)\) and the equation of the line (for the part of the graph that includes \(x=-4\)) is \(y=x + 1\), we substitute \(x=-4\) into the equation.
\(y=-4 + 1=-3\)

Answer:

\(-3\)