Evaluate Piecewise-Defined Function....1

  • MHB
  • Thread starter mathdad
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In summary, a piecewise-defined function is a mathematical function with different rules or equations that apply to different intervals of the domain. To evaluate it, you must determine which rule applies to the input value and then solve for the output. These functions can have any number of pieces and are useful for modeling real-world situations. To graph a piecewise-defined function, each piece must be graphed separately and then connected to create a continuous graph, paying attention to the domain and range of each piece.
  • #1
mathdad
1,283
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The following function is a piecewise-defined function.

y = -x^2 if -2 < x ≤ 0...upper piece
y = x/2 if 0 < x ≤ 4.. bottom piece

Evaluate when x = 0 and x = 4.

Solution:

For x = 0, we evaluate the upper piece.

y = -(0)^2

y = 0

For x = 4, we evaluate the bottom piece.

y = 4/2

y = 2

Is this correct?
 
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  • #2
Yes, this is correct.
 
  • #3
It feels good to be correct. More questions will be posted tomorrow as I travel through David Cohen's precalculus textbook.
 

FAQ: Evaluate Piecewise-Defined Function....1

What is a piecewise-defined function?

A piecewise-defined function is a mathematical function that is defined by different formulas or rules for different parts of its domain. This means that the function may have multiple equations or conditions that determine its output for different input values.

How do you evaluate a piecewise-defined function?

To evaluate a piecewise-defined function, you must determine which part of the function's domain the input value falls under. Then, use the corresponding formula or rule to calculate the output for that specific input value. Repeat this process for all other parts of the domain if necessary.

What is the purpose of using a piecewise-defined function?

Piecewise-defined functions are useful for representing complex relationships or situations where a single equation or rule cannot accurately describe the entire domain. They allow for more flexibility in modeling real-world scenarios and can help simplify calculations.

Can a piecewise-defined function have an infinite number of pieces?

Yes, a piecewise-defined function can have an infinite number of pieces. This is because there is no limit to how many different rules or equations can be used to define different parts of the function's domain.

How do you graph a piecewise-defined function?

To graph a piecewise-defined function, you can plot the points for each part of the function's domain using the corresponding formula or rule. Then, connect the points to create a continuous graph. You may also need to add additional points or lines to represent any discontinuities or changes in the function's behavior.

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