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.
1.All functions have a dependent variable.
2. All functions have an independent variable.
3.A horizontal line is an example of a functional relationship.
yes
yes
no. consider y = 1/x^2
no - it fails the vertical line test
yes
no. consider y = 1/x^2
To determine which statements are true of functions, let's break down each statement and analyze its validity:
1. All functions have a dependent variable:
This statement is true. In a mathematical function, there is always a dependent variable, which is the variable being determined as a result of the input.
2. All functions have an independent variable:
This statement is also true. A mathematical function always has an independent variable, which is the variable that is used as the input to the function, determining the value of the dependent variable.
3. The range of a function includes its domain:
This statement is false. The range of a function refers to the set of all possible values of the dependent variable, whereas the domain refers to the set of all possible values of the independent variable. The range may or may not include all the values of the domain.
4. A vertical line is an example of a functional relationship:
This statement is false. A functional relationship is one where each input value (independent variable) corresponds to one and only one output value (dependent variable). In the case of a vertical line, there are multiple values of the dependent variable associated with a single value of the independent variable, violating the definition of a function.
5. A horizontal line is an example of a functional relationship:
This statement is true. A horizontal line is an example of a functional relationship because for every input value (independent variable), there is only one corresponding output value (dependent variable). Thus, it satisfies the definition of a function.
6. Each output value of a function can correspond to only one input value:
This statement is true. One of the defining characteristics of a function is that each input value (independent variable) corresponds to exactly one output value (dependent variable). There are no multiple outputs associated with a single input value in a function.
Based on the analysis above, the true statements of functions are:
- All functions have a dependent variable.
- All functions have an independent variable.
- A horizontal line is an example of a functional relationship.
- Each output value of a function can correspond to only one input value.