Domain and Range of Relations from Graphs

Domain: $x$ ranges from point $A(-2, -4)$ to $B(4, -6)$:

\[ -2 \le x \le 4 \]

Range: The lowest point is $B(4, -6)$ and highest is $C(2, 2)$:

\[ -6 \le y \le 2 \]

Is it a function? Yes. No vertical line crosses the graph more than once.

Domain: Smallest $x$ at $A(-3, -5)$, largest at $B(8, 4)$:

\[ -3 \le x \le 8 \]

Range: Smallest $y$ at $A(-5)$, largest at $B(4)$:

\[ -5 \le y \le 4 \]

Is it a function? Yes, it passes the vertical line test.

Domain: From $A(-3, -2)$ to $B(1, -2)$:

\[ -3 \le x \le 1 \]

Range: Lowest point $C(-1, -5)$ to highest point $D(-1, 1)$:

\[ -5 \le y \le 1 \]

Is it a function? No. A vertical line crosses the graph at multiple points.

Domain: Leftmost point is $A(-3, 0)$. The arrow points infinitely to the right:

\[ x \ge -3 \]

Range: Lowest points are $B, C$ at $y = -2$. The arrow points up:

\[ y \ge -2 \]

Is it a function? Yes.

Domain: Leftmost is $A(-2, -3)$ with an open circle. Graph extends right:

\[ x > -2 \]

Range: Lowest is $y = -3$ (excluded). Graph extends up:

\[ y > -3 \]

Is it a function? Yes.

Domain: From $A(-8, -0.5)$ to $B(4, 0)$:

\[ -8 \le x \le 4 \]

Range: Lowest point $C(-3, -5)$ to highest $B(4, 0)$:

\[ -5 \le y \le 0 \]

Function: Yes.

Domain: $A(-2, 4)$ to $B(4, 6)$:

\[ -2 \le x \le 4 \]

Range: Lowest $C(2, -2)$ to highest $B(4, 6)$:

\[ -2 \le y \le 6 \]

Function: Yes.

Domain: Extends infinitely left, ends at $A(4, 2)$:

\[ x \le 4 \]

Range: Lowest $y = -2$ (points B and C), extends infinitely up:

\[ y \ge -2 \]

Function: Yes.

Domain: From $A(-5, -1)$ to $B(1, -1)$:

\[ -5 \le x \le 1 \]

Range: Lowest $C(-2, -3)$ to highest $D(-2, 1)$:

\[ -3 \le y \le 1 \]

Function: No. This is a closed curve; vertical lines hit it twice.

Domain: Starts at $A(-3, 1.8)$ with an open circle, extends infinitely right:

\[ x > -3 \]

Range: Highest is $B(-2, 2)$, extends infinitely down:

\[ y \le 2 \]

Function: Yes.