Problemas
Avel used the vertical line test on this graph, and decided is Avel's statement correct? it is a function because the vertical line only passes through one point, (3,0) x Yes, because the vertical line shows that an input has exactly one output. Yes, because only one vertical line can be drawn for the test. No, because the relation does not pass the vertical line test for every possible input. My because he drew a horizontal line rather than a vertical line
Roztwór
Margarita
élite · Tutor durante 8 años
4.6
(275 Votos)
Respuesta
To determine if a graph represents a function, we use the vertical line test. The vertical line test states that if any vertical line drawn through the graph intersects the graph at more than one point, then the graph does not represent a function. Conversely, if every vertical line intersects the graph at most once, then the graph represents a function.Let's analyze the given options:1. **Yes, because the vertical line shows that an input has exactly one output.** - This statement is correct if the vertical line test is passed for all possible inputs (x-values). If every vertical line intersects the graph at most once, it means each input (x-value) has exactly one output (y-value).2. **Yes, because only one vertical line can be drawn for the test.** - This statement is incorrect. The vertical line test requires checking multiple vertical lines across different x-values, not just one.3. **No, because the relation does not pass the vertical line test for every possible input.** - This statement would be correct if there exists at least one vertical line that intersects the graph at more than one point. However, based on the information provided, Avel's statement suggests that the vertical line passes through only one point, indicating that the graph might pass the vertical line test.4. **My because he drew a horizontal line rather than a vertical line.** - This statement is irrelevant to the vertical line test. The vertical line test specifically involves drawing vertical lines, not horizontal ones.Given the information that the vertical line only passes through one point,
, and assuming this is true for all other points on the graph, the correct answer would be:**Yes, because the vertical line shows that an input has exactly one output.**This indicates that the graph passes the vertical line test and thus represents a function.