Narration: A piecewise function is written so that each piece over the specified domain is emphasized.
Image description: f of x equals a behavioral piece across a given domain, another behavior piece across a given domain, another behavioral piece across a given domain, etc.
Narration: Here is an example of a piecewise function and its corresponding graph.
Image description: f of x equals negative 2 plus 5 when x is less than or equal to 2, x squared minus 8x plus 11 when x is greater than two but less than 7, and 8 when x is less than 7. The graph shows a coordinate grid with both the x and y axis extending from negative 10 to 10. The y axis is labeled f of x. A line is graphed with a y-intercept of 5 and a slope of negative 2, ending with a solid point at (2, 1). A parabola is graphed opening up extending from (2, negative 1) and (7, 4), with open dots at these points. A horizontal line extends from a solid point at (7, 8) and extends to infinity.
Narration: This function has two linear pieces and one quadratic piece.
Image description: The same graph appears with the lines identified as linear pieces and the parabola identified as the quadratic piece.
Narration: Each piece of the function is graphed only over the specified domain.
Image description: The function pieces of f of x are negative 2x plus 5, x squared minus 8x plus 11, and 8. The domains are x is less than or equal to 2, x is greater than 2 and less than 7, and x is greater than or equal to 7, respectively. The same graph of the function pieces is shown.
Narration: Graphing piecewise functions is no more difficult than graphing each one of their functional pieces.