Here are the essential concepts you must grasp in order to answer the question correctly.
Function Notation
Function notation, such as ƒ(x), represents a mathematical relationship where 'x' is the input and ƒ(x) is the output. Understanding this notation is crucial for evaluating functions at specific values, such as ƒ(x+h), which involves substituting 'x+h' into the function to find the new output.
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Difference Quotient
The difference quotient is a fundamental concept in calculus that represents the average rate of change of a function over an interval. It is expressed as [ƒ(x+h) - ƒ(x)]/h, where 'h' is the change in 'x'. This concept is essential for understanding the derivative, which measures instantaneous rates of change.
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Polynomial Functions
Polynomial functions, like ƒ(x) = x² + 3x + 1, are expressions that involve variables raised to whole number powers. They are characterized by their degree, which is the highest power of 'x'. Analyzing polynomial functions is important for performing operations such as finding values at specific points and understanding their behavior as 'x' changes.
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