domain and range of graphs practice worksheet ANSWERS - Free Printable

To solve this problem, we need to match each domain and range description with the corresponding graph labeled from A to L. Let's analyze each problem step by step.

Problem 1

- Domain: \(-4 \leq x \leq 4\)
- Range: \(-4 \leq y \leq 4\)
- Function: NO

This describes a relation where both \(x\) and \(y\) are bounded within the same interval, but it is not a function. This suggests a graph that is not a vertical line test pass (i.e., some \(x\) values have multiple \(y\) values). A possible graph could be a circle or an ellipse centered at the origin.

Problem 2

- Domain: \(-3 < x \leq 5\)
- Range: \(y = -1\)
- Function: YES

This describes a horizontal line at \(y = -1\) where \(x\) ranges from \(-3\) to \(5\), excluding \(-3\). The graph will be a horizontal line segment.

Problem 3

- Domain: \(-4 \leq x \leq 2\)
- Range: \(-2 \leq y \leq 4\)
- Function: YES

This describes a function where \(x\) ranges from \(-4\) to \(2\) and \(y\) ranges from \(-2\) to \(4\). The graph will be a curve or a line that passes the vertical line test within this domain.

Problem 4

- Domain: \(x > 0\)
- Range: \(y = 4\)
- Function: YES

This describes a horizontal line at \(y = 4\) where \(x\) is greater than \(0\). The graph will be a horizontal ray starting from \(x = 0\) and extending to the right.

Problem 5

- Domain: \(-6 \leq x \leq 6\)
- Range: \(0 \leq y \leq 6\)
- Function: YES

This describes a function where \(x\) ranges from \(-6\) to \(6\) and \(y\) ranges from \(0\) to \(6\). The graph will be a curve or a line that passes the vertical line test within this domain.

Problem 6

- Domain: \(x = -5\)
- Range: \(-2 < y < 6\)
- Function: NO

This describes a vertical line at \(x = -5\) where \(y\) ranges from \(-2\) to \(6\), excluding \(-2\) and \(6\). The graph will be a vertical line segment.

Problem 7

- Domain: \(x \geq 0\)
- Range: All real numbers
- Function: NO

This describes a relation where \(x\) is non-negative and \(y\) can be any real number. The graph will be a set of points or a curve that does not pass the vertical line test for \(x \geq 0\).

Problem 8

- Domain: \(-3 \leq x \leq 4\)
- Range: \(-2 \leq y \leq 4\)
- Function: NO

This describes a relation where \(x\) ranges from \(-3\) to \(4\) and \(y\) ranges from \(-2\) to \(4\). The graph will be a curve or a set of points that does not pass the vertical line test within this domain.

Problem 9

- Domain: All real numbers
- Range: All real numbers
- Function: YES

This describes a function where both \(x\) and \(y\) can be any real number. The graph will be a curve or a line that passes the vertical line test for all \(x\).

Matching the Graphs

Without seeing the actual graphs, we can infer the following based on the descriptions:

1. Problem 1: Likely a circle or ellipse (Graph L).
2. Problem 2: Horizontal line segment (Graph B).
3. Problem 3: Function with bounded domain and range (Graph F).
4. Problem 4: Horizontal ray (Graph D).
5. Problem 5: Function with bounded domain and range (Graph G).
6. Problem 6: Vertical line segment (Graph C).
7. Problem 7: Relation with \(x \geq 0\) and all \(y\) (Graph H).
8. Problem 8: Relation with bounded domain and range (Graph I).
9. Problem 9: Function with all real numbers for domain and range (Graph K).

Final Answer

\[
\boxed{L, B, F, D, G, C, H, I, K}
\]