This worksheet provides practice problems for evaluating functions based on their graphical representations across four distinct examples.

To solve the problems, we need to evaluate the functions from the given graphs. Let's go through each graph step by step.

Graph 1:

- Equation of the line: The line is a straight line passing through the origin with a slope of 1. Therefore, the equation is \( f(x) = x \).

#### Questions:
1. \( f(3) = \)
- Substitute \( x = 3 \) into \( f(x) = x \):
\[
f(3) = 3
\]

2. \( f(x) = -3 \), \( x = \)
- Solve for \( x \) when \( f(x) = -3 \):
\[
f(x) = x \implies x = -3
\]

Graph 2:

- Shape of the graph: This is a V-shaped graph (absolute value function shifted and scaled). The vertex is at \( (-1, 3) \), and the slopes are symmetric.

#### Questions:
1. \( f(2) = \)
- Locate \( x = 2 \) on the graph. The corresponding \( y \)-value is \( -1 \):
\[
f(2) = -1
\]

2. \( f(x) = 3 \), \( x = \)
- Find the \( x \)-values where the graph intersects \( y = 3 \). From the graph, this occurs at \( x = -1 \):
\[
f(x) = 3 \implies x = -1
\]

Graph 3:

- Shape of the graph: This is a piecewise linear graph with a flat segment.

#### Questions:
1. \( f(-1) = \)
- Locate \( x = -1 \) on the graph. The corresponding \( y \)-value is \( 2 \):
\[
f(-1) = 2
\]

2. \( f(x) = -2 \), \( x = \)
- Find the \( x \)-values where the graph intersects \( y = -2 \). From the graph, this occurs at \( x = -4 \):
\[
f(x) = -2 \implies x = -4
\]

Graph 4:

- Shape of the graph: This is a parabolic graph opening downwards with a vertex at \( (0, 5) \).

#### Questions:
1. \( f(0) = \)
- Locate \( x = 0 \) on the graph. The corresponding \( y \)-value is \( 5 \):
\[
f(0) = 5
\]

2. \( f(x) = 5 \), \( x = \)
- Find the \( x \)-values where the graph intersects \( y = 5 \). From the graph, this occurs at \( x = 0 \):
\[
f(x) = 5 \implies x = 0
\]

Final Answers:

\[
\boxed{
\begin{array}{ll}
f(3) = 3 & f(2) = -1 \\
f(x) = -3, \, x = -3 & f(x) = 3, \, x = -1 \\
f(-1) = 2 & f(0) = 5 \\
f(x) = -2, \, x = -4 & f(x) = 5, \, x = 0 \\
\end{array}
}
\]