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.

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.

 

24 students walk to school