Questions: For each graph below, state whether it represents a function.

Transcript text: For each graph below, state whether it represents a function.

Solution

Solution Steps

To determine if a graph represents a function, we can use the vertical line test. If any vertical line intersects the graph at more than one point, then the graph does not represent a function. We can write a Python function to simulate this test by checking if any x-value corresponds to more than one y-value.

Step 1: Define the Vertical Line Test

To determine if a graph represents a function, we use the vertical line test. This test states that if any vertical line intersects the graph at more than one point, then the graph does not represent a function.

Step 2: Apply the Vertical Line Test to Graph 1

For the graph represented by the points \((1, 2)\), \((2, 3)\), and \((3, 4)\), we check if any \(x\)-value corresponds to more than one \(y\)-value.

For \(x = 1\), \(y = 2\)
For \(x = 2\), \(y = 3\)
For \(x = 3\), \(y = 4\)

Since each \(x\)-value corresponds to exactly one \(y\)-value, the graph passes the vertical line test.

Step 3: Apply the Vertical Line Test to Graph 2

For the graph represented by the points \((1, 2)\), \((1, 3)\), and \((2, 4)\), we check if any \(x\)-value corresponds to more than one \(y\)-value.

For \(x = 1\), \(y = 2\) and \(y = 3\)
For \(x = 2\), \(y = 4\)

Since \(x = 1\) corresponds to two different \(y\)-values (2 and 3), the graph does not pass the vertical line test.

Final Answer

\(\boxed{\text{Graph 1: Function, Graph 2: Not a Function}}\)

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