Question

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.
Avertical 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

All functions have a dependent variable. TRUE

All functions have an independent variable. TRUE

The range of a function includes its domain. FALSE

[Range refers to the set of outputs the function produces, domain the set of inputs the function accepts. They don't really have to have anything to do with each other.]

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

[For a function, each input (x value) maps to at most one output (y value). A vertical line has lots of ys for a single x.]

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

[It's a constant function.]

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

[A function can have the same output given different inputs, for example f(x)=x^2 has f(1)=f(-1) ]