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What is a function in math? What is not a function on a graph?

a) A function is a relation where each input has a unique output.
b) A function is a mathematical operation.
c) A non-function on a graph is a straight line.
d) A non-function on a graph is a relation where an input has multiple outputs.

User Geovanna
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Answer:

Step-by-step explanation:

A function in math is a relation where each input (or x-value) corresponds to a unique output (or y-value). This means that for every input, there is only one output. For example, the equation y = 2x is a function because for every x-value you input, there is a unique y-value that corresponds to it.

On the other hand, a non-function on a graph is a relation where an input (or x-value) has multiple outputs (or y-values). This violates the rule that each input should have a unique output. For example, a vertical line on a graph, such as x = 3, is not a function because it passes through multiple y-values for the same x-value.

To summarize:

- Option a) A function is a relation where each input has a unique output. This is a correct definition of a function.

- Option b) A function is a mathematical operation. This is not an accurate definition of a function. A function is a relation, not an operation.

- Option c) A non-function on a graph is a straight line. This is not accurate. A straight line can be a function or a non-function depending on whether each input has a unique output.

- Option d) A non-function on a graph is a relation where an input has multiple outputs. This is an accurate definition of a non-function on a graph. It violates the rule of having a unique output for each input

User Dilini Rajapaksha
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Final answer:

A function in math defines a unique output for each input, and is often used in economic models to describe relationships. On a graph, a function is represented by a line where each x-coordinate corresponds to one y-coordinate only. A non-function occurs when an input has multiple outputs, such as a vertical line on a graph.

Step-by-step explanation:

A function in math is a special type of relationship between values, where each input (often called an independent variable) is associated with exactly one output (often called a dependent variable). When we express economic models, functions help to represent these relationships. For instance, if we say 'Professor = Adam Smith', we're defining a relationship where the term 'Professor' functionally relates to 'Adam Smith'. Similarly, 'Friends = Bob + Shawn + Margaret' represents a summation of friends creating a group.

On a graph, a line can represent a function if for every input value (x-coordinate), there is only one output value (y-coordinate). This follows the mathematical form of a linear equation, for example, y = mx + b or y = a + bx, where m or b represents the slope of the line and b or a represents the y-intercept, respectively. However, if a graphed line is vertical, it means for some input x, there are multiple output y values, which violates the definition of a function.

Therefore, a non-function on a graph is a relation where an input has multiple outputs. An example of this would be a vertical line, which does not pass the vertical line test; if any vertical line intersects the graph in more than one point, the graph does not represent a function.

User Jeremyosborne
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