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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