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Which statements are true of functions? Check all that apply.

A. All functions have a dependent variable.

B. All functions have an independent variable.

C. The range of a function includes its domain.

D. A vertical line is an example of a functional relationship.

E. A horizontal line is an example of a functional relationship.

F. Each output value of a function can correspond to only one input value.

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Answer:

The correct options are:

A. All functions have a dependent variable.

B. All functions have an independent variable.

E. A horizontal line is an example of a functional relationship.

Step-by-step explanation:

All functions have atleast a dependent variable.

If we write a function y=f(x) then it means that y depends on the value of x. This shows that y is dependent variable and x is independent variable.

A horizontal line is an example of a functional relationship because given a value of x, you can always tell the value of y.

The correct options are A,B and E....

Answer:

The true statements are:

A.   All functions have a dependent variable.

B.   All functions have an independent variable.

E.    A horizontal line is an example of a functional relationship.

Step-by-step explanation:

  • A relation is a function if each x has a single image i.e. each x is mapped to a single y-value.
  • Also, the function must always satisfy the vertical line test i.e. any line passing through the domain and parallel to the y-axis should intersect the curve exactly once.
  • Also, a function corresponding to variable x is defined by:

                                y=f(x)

where x is the independent variable because it's value will be assigned and y is the dependent variable because it's value is obtained corresponding to each value of x.

  • Also, a vertical line is not a function ( since it does not passes the vertical line test )

whereas a horizontal line is a function ( as it passes the vertical line test ).

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