Here are the essential concepts you must grasp in order to answer the question correctly.
Function Evaluation
Function evaluation involves substituting a specific value into a function to determine its output. In this case, evaluating ƒ(x+h) means replacing 'x' in the function ƒ(x) = 1 - x² with 'x+h'. This process is fundamental in calculus and algebra as it lays the groundwork for understanding how functions behave as their inputs change.
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Difference Quotient
The difference quotient is a formula that represents the average rate of change of a function over an interval. It is calculated as [ƒ(x+h) - ƒ(x)]/h, where 'h' is the change in 'x'. This concept is crucial for understanding derivatives in calculus, as it approximates the slope of the tangent line to the function at a point.
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Limit Concept
The limit concept is essential in calculus, describing the behavior of a function as its input approaches a certain value. In the context of the difference quotient, as 'h' approaches zero, the expression [ƒ(x+h) - ƒ(x)]/h approaches the derivative of the function at 'x'. This concept is foundational for defining derivatives and understanding instantaneous rates of change.
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