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Which statements are true of functions? Check all that apply. All functions have a dependent variable. All functions have an independent variable. The range of a function includes its domain. A vertical line is an example of a functional relationship. A horizontal line is an example of a functional relationship. Each output value of a function can correspond to only one input value

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Answer:

First option: All functions have dependent variable (At least)

Second option: All functions have an independent variable.

Fifth option: A horizontal line is an example of a functional relationship.

Step-by-step explanation:

By definition, a relation is a function if each input value has one and only one output value.

A function have a at least a dependent variable and an independent variable. For example, given a function:

 [tex]y=x[/tex]

The dependent variable is "y"  and the independent variable is "x".

The Domain of the function is the set of possible input values and the Range is the set of possible output values,

Vertical lines have undefined slope. Since the value of "x" never changes, a vertical line is not an example of a functional relationship.

In the case of Horizontal lines, for any x-value you get the same y-value. These are called "Constant functions".

Based on this, the following statements are true:

  • All functions have a dependent variable (At least).
  • All functions have an independent variable.
  • A horizontal line is an example of a functional relationship.
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Function is a type of relation between domain and range. In general, statements 1, 2 and 5 are correct about the function.

Function is a type of relation in which one input value is connected with only one output value. Though, one output can have multiple inputs.

Following are the properties of a function:

  • Domain of a function is the input value of the function. Generally, x value is taken as domain or input.
  • Range is the output value of the function. It is generally taken as y coordinate.
  • Domain and range need not always be the same or a subset of one another.
  • Function always has at least one dependent variable (range) and independent variable (domain).

Now, if we are taking x coordinate as domain or independent variable, then the vertical line is not a function because it has multiple outputs for only one input but a horizontal line can be a function. If we interchange the dependent and independent variables, then the vertical line can be a function.

So, the correct statements are:

  • All functions have a dependent variable.
  • All functions have an independent variable.
  • A horizontal line is an example of a functional relationship.

Therefore, in general, statements 1, 2, and 5 are correct about the function.

For more details, refer to the link:

https://brainly.com/question/15536992

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