We need to determine which of the given relations are functions. We are given two relations as sets of ordered pairs and two relations as graphs. A relation is a function if each input (x-value) has only one output (y-value).

1. Problem Description

We need to determine which of the given relations are functions. We are given two relations as sets of ordered pairs and two relations as graphs. A relation is a function if each input (x-value) has only one output (y-value).

2. Solution Steps

a) The given relation is {(-2,-1), (-1,2), (0,1), (-1,3)}. We see that the input -1 has two different outputs, 2 and

3. Therefore, this relation is not a function.

b) The given relation is {(-2,-1), (-1,-1), (0,1), (1,0)}. Each input has a unique output. Therefore, this relation is a function.

c) The graph is a piecewise linear function. We can apply the vertical line test. Any vertical line drawn on the graph will intersect the graph at only one point. Therefore, this graph represents a function.

d) The graph is a sideways parabola. If we apply the vertical line test, we see that a vertical line can intersect the graph at two points. For instance, a vertical line at $x=1$ intersects the graph at two different $y$ values. Therefore, this graph does not represent a function.

3. Final Answer

The relations that are functions are b) and c).