9 Best Worksheets For Identifying The Domain And Range Of ... - Free Printable
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Step-by-step solution for: 9 Best Worksheets For Identifying The Domain And Range Of ...
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Step-by-step solution for: 9 Best Worksheets For Identifying The Domain And Range Of ...
This image displays a set of 12 graphs on Cartesian coordinate planes, arranged in a 4x3 grid. The task is to determine which of these graphs represent functions.
To solve this, I will use the Vertical Line Test. A graph represents a function if and only if every vertical line intersects the graph at most once. If any vertical line crosses the graph at more than one point, it fails the test and is not a function.
I will now analyze each graph one by one to apply this test.
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- Graph 1 (Top Left): This graph consists of two separate vertical lines (one at x=-2 and one at x=2). Any vertical line drawn at x=-2 or x=2 will intersect the graph infinitely many times. Not a function.
- Graph 2 (Top Middle): This is a piecewise linear graph. Drawing any vertical line will intersect it at exactly one point. It is a function.
- Graph 3 (Top Right): This is a smooth, continuous curve that passes the vertical line test. No vertical line will intersect it more than once. It is a function.
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- Graph 4 (Second Row, Left): This graph is a horizontal line with arrows on both ends, indicating it extends infinitely. A vertical line will intersect it at exactly one point. It is a function.
- Graph 5 (Second Row, Middle): This graph consists of five distinct points. Since no two points share the same x-coordinate, any vertical line will intersect at most one point. It is a function.
- Graph 6 (Second Row, Right): This is a curve that appears to be part of a parabola opening to the left. A vertical line drawn at any x-value between -5 and 0 will intersect the curve at exactly one point. It is a function.
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- Graph 7 (Third Row, Left): This is a circle centered at the origin. A vertical line drawn through the center (e.g., x=0) will intersect the circle at two points (top and bottom). Not a function.
- Graph 8 (Third Row, Middle): This is a wavy, periodic-looking curve. It passes the vertical line test; every vertical line intersects it at only one point. It is a function.
- Graph 9 (Third Row, Right): This is a multi-segmented line graph. There are several x-values where a vertical line would intersect the graph at two different y-values (for example, at x=0, the line goes from y=2 down to y=-2, and then back up). Not a function.
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- Graph 10 (Bottom Left): This is a V-shaped graph, similar to an absolute value function. Every vertical line intersects it at exactly one point. It is a function.
- Graph 11 (Bottom Middle): This is a piecewise graph with open and closed circles. At x=0, there is an open circle at y=1 and a closed circle at y=-1. At x=2, there is an open circle at y=1 and a closed circle at y=0. For any given x, there is only one corresponding y-value (the closed circle defines the value). It is a function.
- Graph 12 (Bottom Right): This is a triangle shape. A vertical line drawn through the middle of the triangle (e.g., at x=1) will intersect the graph at two points (one on the top edge and one on the bottom edge). Not a function.
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The graphs that represent functions are:
- Graph 2
- Graph 3
- Graph 4
- Graph 5
- Graph 6
- Graph 8
- Graph 10
- Graph 11
The graphs that do not represent functions are:
- Graph 1
- Graph 7
- Graph 9
- Graph 12
This conclusion is based on the application of the Vertical Line Test to each graph.
To solve this, I will use the Vertical Line Test. A graph represents a function if and only if every vertical line intersects the graph at most once. If any vertical line crosses the graph at more than one point, it fails the test and is not a function.
I will now analyze each graph one by one to apply this test.
---
First Row
- Graph 1 (Top Left): This graph consists of two separate vertical lines (one at x=-2 and one at x=2). Any vertical line drawn at x=-2 or x=2 will intersect the graph infinitely many times. Not a function.
- Graph 2 (Top Middle): This is a piecewise linear graph. Drawing any vertical line will intersect it at exactly one point. It is a function.
- Graph 3 (Top Right): This is a smooth, continuous curve that passes the vertical line test. No vertical line will intersect it more than once. It is a function.
---
Second Row
- Graph 4 (Second Row, Left): This graph is a horizontal line with arrows on both ends, indicating it extends infinitely. A vertical line will intersect it at exactly one point. It is a function.
- Graph 5 (Second Row, Middle): This graph consists of five distinct points. Since no two points share the same x-coordinate, any vertical line will intersect at most one point. It is a function.
- Graph 6 (Second Row, Right): This is a curve that appears to be part of a parabola opening to the left. A vertical line drawn at any x-value between -5 and 0 will intersect the curve at exactly one point. It is a function.
---
Third Row
- Graph 7 (Third Row, Left): This is a circle centered at the origin. A vertical line drawn through the center (e.g., x=0) will intersect the circle at two points (top and bottom). Not a function.
- Graph 8 (Third Row, Middle): This is a wavy, periodic-looking curve. It passes the vertical line test; every vertical line intersects it at only one point. It is a function.
- Graph 9 (Third Row, Right): This is a multi-segmented line graph. There are several x-values where a vertical line would intersect the graph at two different y-values (for example, at x=0, the line goes from y=2 down to y=-2, and then back up). Not a function.
---
Fourth Row
- Graph 10 (Bottom Left): This is a V-shaped graph, similar to an absolute value function. Every vertical line intersects it at exactly one point. It is a function.
- Graph 11 (Bottom Middle): This is a piecewise graph with open and closed circles. At x=0, there is an open circle at y=1 and a closed circle at y=-1. At x=2, there is an open circle at y=1 and a closed circle at y=0. For any given x, there is only one corresponding y-value (the closed circle defines the value). It is a function.
- Graph 12 (Bottom Right): This is a triangle shape. A vertical line drawn through the middle of the triangle (e.g., at x=1) will intersect the graph at two points (one on the top edge and one on the bottom edge). Not a function.
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Final Answer
The graphs that represent functions are:
- Graph 2
- Graph 3
- Graph 4
- Graph 5
- Graph 6
- Graph 8
- Graph 10
- Graph 11
The graphs that do not represent functions are:
- Graph 1
- Graph 7
- Graph 9
- Graph 12
This conclusion is based on the application of the Vertical Line Test to each graph.
Parent Tip: Review the logic above to help your child master the concept of finding domain and range of a graph worksheet.
