Question

1. given the function, what is $f(-4)$?

Explanation:

Step1: Find the slope of the line

First, identify two points on the line. From the graph, we can see that the line passes through \((2, 0)\) and \((0, -1)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((2, 0)\) and \((0, -1)\), we have \(m=\frac{0 - (-1)}{2 - 0}=\frac{1}{2}\).

Step2: Find the equation of the line

Using the slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. From the point \((0, -1)\), we know that \(b=-1\). So the equation of the line is \(y=\frac{1}{2}x - 1\), which is the function \(f(x)=\frac{1}{2}x - 1\).

Step3: Calculate \(f(-4)\)

Substitute \(x = - 4\) into the function \(f(x)=\frac{1}{2}x - 1\). We get \(f(-4)=\frac{1}{2}\times(-4)-1\). First, calculate \(\frac{1}{2}\times(-4)=-2\). Then, \(-2-1=-3\).

Answer:

\(-3\)