ANSWER
\(f( - 1) = 3\)
EXPLANATION
Method 1
We can determine that,
\(f( - 1) = 3\)
by tracing directly from the graph as shown in the attachment.
Method 2.
We can find the equation of the line first.
The graph passes through
(0,1) and (1,-1).
\(slope = \frac{ - 1 - 1}{1 - 0} = - 2\)
The equation of the line is of the form,
\(y =mx + c\)
where
\(m = - 2\)
is the slope and
\(c = 1\)
is the y-intercept.
This implies that,
\(y = - 2x + 1\)
\(f( - 1) = - 2( - 1) + 1\)
We evaluate to get,
\(f( - 1) = 2 + 1 = 3\)
