4.How can you tell if you have a function or not?*
Look for constant
The domain does not repeat
The range does not repeat
The vertical line test
The most straightforward way to determine if you have a function or not is by applying the vertical line test. This means that for every unique x-value in the domain, there should be only one corresponding y-value in the range. If you can draw a vertical line that intersects the graph of the relation in more than one point, then it is not a function.
Answer whith the choices
To determine if you have a function or not, you can consider the following options:
1. Look for a constant: If the relation only consists of a single constant value, it is not considered a function.
2. The domain does not repeat: In a function, each input value (x-value) in the domain should correspond to exactly one output value (y-value) in the range. If any x-value is repeated with different y-values, it is not a function.
3. The range does not repeat: Similarly, in a function, each y-value in the range should correspond to only one x-value in the domain. If any y-value is repeated with different x-values, it is not a function.
4. The vertical line test: This is the most common method to determine if a relation is a function. If you can draw a vertical line on a graph of the relation and it intersects the graph in more than one point, then it is not a function. However, if the vertical line only intersects the graph at one point (even if it touches), then it is a function.
To determine if you have a function or not, you can follow these steps and criteria:
1. Look for a constant: If all the values of the dependent variable (usually denoted by y) are the same for all values of the independent variable (usually denoted by x), then you have a constant function. A constant function is a special type of function where the output does not change regardless of the input.
2. Check for repeating values in the domain: The domain of a function refers to all the possible input values. In a function, each input value (x) should correspond to only one output value (y). If you notice any repeating values in the domain, then you do not have a function.
3. Verify there are no repeating values in the range: The range of a function refers to all the possible output values. In a function, each output value (y) should correspond to only one input value (x). If you observe any repeating values in the range, then you do not have a function.
4. Apply the vertical line test: The vertical line test is a graphical method used to check if a graph represents a function. Simply put, if a vertical line intersects the graph in more than one point, then it does not represent a function. If, on the other hand, each vertical line intersects the graph at most once, then it is a function.
By considering these criteria, you can determine if you have a function or not.