Respuesta :
Answer:
The correct statements that are true to functions are :
- All functions have a dependent variable.
- All functions have an independent variable.
These above two can be explained as : We write a function as y = f(x), where x is the independent variable, and y is dependent as it depends on x values.
- A horizontal line is an example of a functional relationship.
Rest all options are incorrect.
Answer:
The correct options are:
Option A: All functions have a dependent variable.
Option B: All functions have an independent variable.
Option E: A horizontal line is an example of a functional relationship.
Step-by-step explanation:
Consider the provided information.
Function: A function is a relationship where each input has only one output.
Which is denoted by "y=f(x)" where x is input value, also the variable x is independent and y is dependent.
Each input value has exactly one output value vice versa is not true.
Vertical line test: A equation is said to be a function if all vertical lines intersect the graph at most once.
Now consider the provided options:
Option A: All functions have a dependent variable.
This option is true, by the above definition of function.
Option B: All functions have an independent variable.
This option is true, by the above definition of function.
Option C: The range of a function includes its domain.
This option is false.
Understand this with the help of an example:
Consider the function [tex]y=x^2[/tex]
The range of the function is [0,∞) and domain of the function (-∞,∞).
Here range doesn't contains the domain.
Thus this option is wrong.
Option D: vertical line is an example of a functional relationship.
The equation of the vertical line is x=a where a can be any real number.
We have different values of y for a unique x also the function fails the vertical line test.
Thus the option D is False.
Option E: A horizontal line is an example of a functional relationship.
The equation of horizontal line is y=a where a can be any real number.
For each input has only one output also it satisfy the vertical line test. We will have same value of y for any x. Which satisfy the property of function.
Thus this option is true.
Option F: Each output value of a function can correspond to only one input value by definition of function.
Understand this with the help of an example:
Consider the function y=a
The function has same output value for each input value. Which is the contradictory to the option's statement.
Thus, this option is false.
The correct options are:
Option A: All functions have a dependent variable.
Option B: All functions have an independent variable.
Option E: A horizontal line is an example of a functional relationship.
