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.

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

x equals 1

step-by-step explanation:

f(4)=f(×)

x=1

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: