Question

find the value of $f(-3)$.
$y = f(x)$
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attempt 1 out of 2
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Explanation:

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

The left - most line (the linear part on the left) is the relevant part of the graph for \( x=-3 \). Let's find the equation of this line. We can see that this line passes through two points, for example, when \( x = - 5 \), \( y = 0 \) (the x - intercept) and when \( x=0 \), \( y=-5 \) (the y - intercept). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-5 - 0}{0-(-5)}=\frac{-5}{5}=- 1 \). Using the slope - intercept form \( y=mx + b \), where \( b=-5 \) (the y - intercept), the equation of the line is \( y=-x - 5 \).

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

Substitute \( x = - 3 \) into \( y=-x - 5 \). We get \( y=-(-3)-5=3 - 5=-2 \). Alternatively, we can look at the graph. For \( x=-3 \), we find the corresponding \( y \) - value on the graph of \( y = f(x) \). By moving vertically from \( x=-3 \) to the graph and then horizontally to the \( y \) - axis, we can see that the \( y \) - value is - 2.

Answer:

\(-2\)