Linear Functions Domain: and Range: and Inequality Notation: and Interval Notation: and add an example for all 4 of them
Domain: The set of all possible input values for a linear function. It is often expressed as the set of all real numbers unless there are restrictions on the input values.
Example: Consider the linear function f(x) = 3x + 2. The domain of this function is all real numbers because there are no restrictions on the input values.
Range: The set of all possible output values for a linear function. It is often expressed as the set of all real numbers unless there are restrictions on the output values.
Example: Consider the linear function f(x) = 3x + 2. The range of this function is all real numbers because there are no restrictions on the output values.
Inequality Notation: An alternative way to express the domain and range of a function using inequalities. It typically involves specifying conditions or restrictions on the input or output values.
Example (Inequality Notation for Domain): Consider the linear function f(x) = 3x + 2. In inequality notation, the domain can be expressed as x ≥ -∞, which means x is greater than or equal to negative infinity.
Example (Inequality Notation for Range): Consider the linear function f(x) = 3x + 2. In inequality notation, the range can be expressed as y ≥ -∞, which means y is greater than or equal to negative infinity.
Interval Notation: Another way to express the domain and range of a function using intervals. It involves specifying a range or set of values within a specific interval.
Example (Interval Notation for Domain): Consider the linear function f(x) = 3x + 2. In interval notation, the domain can be expressed as (-∞, ∞), which means all real numbers.
Example (Interval Notation for Range): Consider the linear function f(x) = 3x + 2. In interval notation, the range can be expressed as (-∞, ∞), which means all real numbers.
Linear Functions End Behavior and an example
End Behavior: The end behavior of a linear function describes the behavior of the function as the input values approach positive or negative infinity. It is determined by the slope of the linear function.
Example: Consider the linear function f(x) = 2x + 1. The slope of this function is 2, indicating that it has a positive slope. As the input values increase towards positive infinity, the function will also increase without bound. Similarly, as the input values decrease towards negative infinity, the function will decrease without bound. Therefore, the end behavior of this linear function is described as increasing without bound as x approaches positive or negative infinity.