Marcar la casilla correspondiente a cada gráfico que represente una función.

Mathematics
Marcar la casilla correspondiente a cada gráfico que represente una función.

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Answer

"Gráfico 1" represents a function

Step 1: Understand the definition of a function using the vertical line test. A graph represents a function if and only if every vertical line drawn through the graph intersects the graph at most once. If a vertical line intersects the graph at two or more points, then it is not a function.

Step 2: Apply the vertical line test to "Gráfico 1". Observe the points plotted on "Gráfico 1": • At x=−3x = -3, there is one point (−3,−1)(-3, -1). • At x=−2x = -2, there is one point (−2,−2)(-2, -2). • At x=−1x = -1, there is one point (−1,2)(-1, 2). • At x=0x = 0, there is one point (0,−1)(0, -1). • At x=1x = 1, there is one point (1,0)(1, 0). • At x=2x = 2, there is one point (2,−2)(2, -2). • At x=3x = 3, there is one point (3,−3)(3, -3).

Step 3: Conclude based on the vertical line test. For every x-value in "Gráfico 1", there is only one corresponding y-value. This means that no vertical line would intersect more than one point on the graph. Therefore, "Gráfico 1" represents a function.

Since only "Gráfico 1" is visible, we can only evaluate this graph.

The graph that represents a function is: Gráfico 1

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Quick Answer

Understand the definition of a function using the vertical line test. A graph represents a function if and only if every vertical line drawn through the graph intersects the graph at most once.

Marcar la casilla correspondiente a cada gráfico que represente una función.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: Understand the definition of a function using the vertical line test. A graph represents a function if and only if every vertical line drawn through the graph intersects the graph at most once. If a vertical line intersects the graph at two or more points, then it is not a function. Step 2: Apply the vertical line test to "Gráfico 1". Observe the points plotted on "Gráfico 1": • At x = -3, there is one point (-3, -1). • At x = -2, there is one point (-2, -2). • At x = -1, there is one point (-1, 2). • At x = 0, there is one point (0, -1). • At x = 1, there is one point (1, 0). • At x = 2, there is one point (2, -2). • At x = 3, there is one point (3, -3). Step 3: Conclude based on the vertical line test. For every x-value in "Gráfico 1", there is only one corresponding y-value. This means that no vertical line would intersect more than one point on the graph. Therefore, "Gráfico 1" represents a function. Since only "Gráfico 1" is visible, we can only evaluate this graph. The graph that represents a function is: Gráfico 1 That's 2 down. 3 left today — send the next one.