Answer: In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element in another set (called the range). The range of a function is the set of all possible output values of the function.
The range of a function can be determined by analyzing the behavior of the function as its input values change. For example, a linear function like f(x) = -3x + 4 has a slope of -3, which means that as x increases, the value of -3x decreases. This in turn means that the value of f(x) decreases as x increases.
Another important consideration in determining the range of a function is the domain of the function. The domain is the set of all possible input values of the function. If the domain is limited in some way (for example, if the function is only defined for non-negative values of x), then the range will also be limited.
In the case of f(x) = -3x + 4, the domain is all real numbers, so the range is also all real numbers. In other words, the function can take on any value on the real number line. This can be written in interval notation as (-∞, +∞) or (-∞, ∞).
I hope this explanation helps you understand the concept of the range of a function more deeply.
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