ANSWER
[tex]f( - 1) = 3[/tex]
EXPLANATION
Method 1
We can determine that,
[tex]f( - 1) = 3[/tex]
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).
[tex]slope = \frac{ - 1 - 1}{1 - 0} = - 2[/tex]
The equation of the line is of the form,
[tex]y =mx + c[/tex]
where
[tex]m = - 2[/tex]
is the slope and
[tex]c = 1[/tex]
is the y-intercept.
This implies that,
[tex]y = - 2x + 1[/tex]
[tex]f( - 1) = - 2( - 1) + 1[/tex]
We evaluate to get,
[tex]f( - 1) = 2 + 1 = 3[/tex]
