Which of the following shows a function?(1 point)

Question

Responses

{ (0, -4) (2, 7) (0, 4) (1, 9) (3, 7)}
The image presents three different representations of mathematical functions:
Graph:
A curve is plotted on a Cartesian coordinate system. This graph visually represents a function, showing the relationship between x and y values. The shape of the curve is not a standard function, like a straight line or parabola, but a more complex, looping shape.
Mapping Diagram:
This diagram uses ovals to represent the input and output sets of a function. Arrows show the relationship between specific input values (2, 4, and 3) and their corresponding output values (20, 30, and 40). It illustrates how each input is mapped to a specific output, demonstrating the function's behavior for these particular values.
Table of Values:
A table lists several x-values, the corresponding calculations using the function y = 2x + 3, the resulting y-values, and the ordered pairs (x, y). This table provides a numerical representation of the function, allowing for precise calculation and easy identification of points on the function's graph. The table demonstrates a linear function, where the y-value increases by 2 for every increase of 1 in the x-value.

Answer 1

To determine which of the provided options shows a function, we need to recall that a function must have the property that for every input (x-value), there is exactly one output (y-value). Let's analyze each option:

1. Set of Points: \[ { (0, -4), (2, 7), (0, 4), (1, 9), (3, 7) } \] In this set, the input \(x = 0\) corresponds to two different outputs: \(y = -4\) and \(y = 4\). Since an input cannot map to more than one output in a function, this set does not represent a function.

2. Graph: The description mentions a curve that is complex and looping. While it does not detail specific coordinates or behaviors, the ability for a curve to return to a previous \(y\)-value for a given \(x\)-value could indicate that it fails the vertical line test. Without a precise visual, we cannot conclude with certainty, but it is important to consider that a complex shape could potentially map a single input to multiple outputs.

3. Mapping Diagram: The diagram shows a clear mapping between specific input values (2, 4, and 3) and their corresponding outputs (20, 30, and 40). Since each input is connected to only one output, this represents a function.

4. Table of Values: The table corresponds to the function \(y = 2x + 3\). In this case, each \(x\)-value produces only one \(y\)-value, confirming that it is indeed a function.

Based on this analysis, the Mapping Diagram and the Table of Values both represent functions. However, since the question asks for "which of the following shows a function," the best answers are the Mapping Diagram and the Table of Values.

If a single choice is needed, choose the Mapping Diagram or the Table depending on the context given (both are valid answers). If limited to just one answer option from a test perspective, confirm how many options can be selected; otherwise, both exhibit the properties of functions.