Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Graph the function, insert solid circles or open circles where necessary to indicate the true nature of the function

### Piecewise Function Example The function \( K(x) \) is defined as a piecewise function with three different expressions depending on the value of \( x \): \[ K(x) = \begin{cases} 1, & \text{if } x \leq -2 \\ x^2 - 4, & \text{if } -2 < x < 2 \\ \frac{1}{2}x, & \text{if } x \geq 2 \end{cases} \] - When \( x \) is less than or equal to -2, \( K(x) \) is equal to 1. - When \( x \) is greater than -2 but less than 2, \( K(x) \) is represented by the quadratic equation \( x^2 - 4 \). - When \( x \) is greater than or equal to 2, \( K(x) \) is equal to half of \( x \). This type of function is called a piecewise function because it is defined by different expressions for different intervals of the domain.
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Transcribed Image Text:### Piecewise Function Example The function \( K(x) \) is defined as a piecewise function with three different expressions depending on the value of \( x \): \[ K(x) = \begin{cases} 1, & \text{if } x \leq -2 \\ x^2 - 4, & \text{if } -2 < x < 2 \\ \frac{1}{2}x, & \text{if } x \geq 2 \end{cases} \] - When \( x \) is less than or equal to -2, \( K(x) \) is equal to 1. - When \( x \) is greater than -2 but less than 2, \( K(x) \) is represented by the quadratic equation \( x^2 - 4 \). - When \( x \) is greater than or equal to 2, \( K(x) \) is equal to half of \( x \). This type of function is called a piecewise function because it is defined by different expressions for different intervals of the domain.
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