Question

question
find the value of $f(6)$.
$y = f(x)$

Explanation:

Step1: Identify the line for \( x \geq 0 \)

For \( x \geq 0 \), the graph is a straight line. We can find its equation using two points. Let's take \( (0, -1) \) and \( (1, -2) \) (or other points on this line). The slope \( m \) is \( \frac{-2 - (-1)}{1 - 0} = -1 \). Using point - slope form \( y - y_1 = m(x - x_1) \) with \( (x_1,y_1)=(0, - 1) \), the equation is \( y=-x - 1 \).

Step2: Substitute \( x = 6 \) into the equation

Substitute \( x = 6 \) into \( y=-x - 1 \). So \( y=-6 - 1=-7 \). So \( f(6)=-7 \).

Answer:

\( -7 \)