Question

find the value of f(-3). y = f(x)

Explanation:

Step1: Identify the line for \( x = -3 \)

The graph of \( y = f(x) \) has a linear part on the left (before the peak). For \( x = -3 \), we use the left - hand linear segment.
First, find the equation of the left - hand line. We can see two points on this line: let's take the x - intercept at \( x=-6 \) (where \( y = 0 \)) and the y - intercept at \( x = 0 \) (where \( y=6 \)). The slope \( m\) of the line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((-6,0)\) and \((0,6)\), we have \( m=\frac{6 - 0}{0-(-6)}=\frac{6}{6} = 1\). The equation of a line in slope - intercept form \( y=mx + b\), where \( b\) is the y - intercept. Here, \( b = 6\), so the equation is \( y=x + 6\).

Step2: Substitute \( x=-3 \) into the equation

Substitute \( x=-3 \) into \( y=x + 6\). Then \( y=-3 + 6=3\). Alternatively, we can directly look at the graph. For \( x=-3\), we move vertically from \( x = - 3\) on the x - axis until we hit the graph of \( f(x)\), and then horizontally to the y - axis. We can see that the y - value (the value of \( f(-3)\)) is 3.

Answer:

\( 3 \)