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ludi_srbin
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Let f(x)=x+|x| and g be defined by the rule "g(x) is the slope of the graph pf f at x".
Write f as piecewise defined function.
Write f as piecewise defined function.
Minor point: don't forget x = 0 in your definition.TD said:Where x > 0, you get f(x) = 2x.
Where x < 0, you get f(x) = 0.
Does that help?
A piecewise defined function is a mathematical function that is defined differently for different parts of its domain. This means that the function may have different rules or equations that apply to different intervals or ranges of input values.
To write a function as a piecewise defined function, you need to specify the different intervals or ranges of input values and the corresponding rules or equations that apply to each interval. The function should also include a default rule for any input values that do not fall within the specified intervals.
A piecewise defined function can be useful for representing a mathematical relationship that changes or behaves differently depending on the input values. This can be particularly helpful in modeling real-world situations or solving complex mathematical problems.
Yes, a piecewise defined function can have any number of pieces, depending on the complexity of the function. There is no limit to the number of pieces that can be used in a piecewise defined function.
To evaluate a piecewise defined function, you need to determine which interval or range the given input value falls within, and then use the corresponding rule or equation to calculate the output value. If the input falls within the default rule, then that rule should be used to calculate the output.