Question

Which statements are true of functions? Check all that apply

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All functions have a dependent vanable
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

Answer 1

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.

Explanation:

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Answer 2

The true statemens are:

All function have (at least) a dependent variable. That is why you can write y = f(x), x is the independent variable, while y depends on x values, so y is the independent variable.

All function have and independent variable (explained above).

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

The other statements are false:

The range of a function includes its domain is false.

Domain are the values that x can take and the range are the values that the function (y) can take. One is not included in the other.

A vertical line is an example of a functional relationship is false, because you can not tell the value of y for any value of x.

Each output value of a function can correspond to only one input value is false. An output can be generated by more than one value of x. The horizontal line is an example of that: the same value of y (output) corresponde to any value of x.

Explanation: