ind the domain of each function. Then determine if the function is increasing, decreasing, or constant over each interval in its domain.Chapter Referencebh x = x − 1 + 5
Question
ind the domain of each function. Then determine if the function is increasing, decreasing, or constant over each interval in its domain.Chapter Referencebh x = x − 1 + 5
Solution
The function given is bh(x) = x - 1 + 5, which simplifies to bh(x) = x + 4.
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Finding the domain of the function: The domain of a function is the set of all possible input values (often x-values) which will output real numbers. In this case, the function is a linear function and there are no denominators, square roots, or logarithms that we need to restrict the domain for. Therefore, the domain of this function is all real numbers, often written as (-∞, ∞).
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Determining if the function is increasing, decreasing, or constant over each interval in its domain: A function is increasing if as x increases, f(x) also increases. It's decreasing if as x increases, f(x) decreases. It's constant if f(x) doesn't change as x increases.
In this case, the function bh(x) = x + 4 is a linear function with a positive slope (1). This means that as x increases, bh(x) also increases. Therefore, the function is increasing over its entire domain.
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