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Domain: The domain of a function is the set of all possible input values (independent variables) for which the function is defined. Range: The range of a function is the set of all possible output values (dependent variables) that the function can produce. Independent Variable: An independent variable is the input variable in a function that can be freely chosen from the domain. It is the variable that is being manipulated to analyze its effect on the dependent variable. Dependent Variable: A dependent variable is the output variable in a function that depends on the value of the independent variable. It is the variable that is being studied or measured in the relationship.

Let's consider the function f(x) = 2x + 3, where x is the independent variable and f(x) is the dependent variable. Step 1: Identify the domain and range Here, the domain of the function is the set of all possible values of x for which the function is defined. In this case, the domain is all the real numbers, denoted by D = (-∞, ∞). The range of the function is the set of all possible values of f(x) that the function can produce. As x can be any real number, f(x) can also be any real number, so the range is also R = (-∞, ∞). Step 2: Evaluate the relationship between the independent and dependent variables In this function, the dependent variable f(x) relies on the value of the independent variable x. For every value of x chosen from the domain, there is a corresponding value of f(x) in the range which is determined by the formula f(x) = 2x + 3. For example: - If x = 1, then f(1) = 2(1) + 3 = 5 - If x = -2, then f(-2) = 2(-2) + 3 = -1 In conclusion, a function relates an independent variable to a dependent variable by defining a rule that assigns each value from the domain to a unique value in the range. The independent variable represents the input values of a function, while the dependent variable represents the output values, which are determined by the function's rule.