Flashcard #6 Review-Piecewise Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

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How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which piece of the function applies to that point and use the corresponding expression.

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What does the graph of a piecewise function look like?

Back

The graph of a piecewise function may consist of multiple segments, each representing a different expression, and can include jumps or breaks.

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What is the importance of domain in piecewise functions?

Back

The domain of a piecewise function specifies the intervals for which each piece of the function is valid.

Front

How can you represent a piecewise function mathematically?

Back

A piecewise function can be represented using braces, with each piece defined for its specific interval, e.g., f(x) = { x^2 for x < 0, x + 1 for x >= 0 }.

Front

What is a distance-time graph?

Back

A distance-time graph shows the distance traveled over time, where the x-axis represents time and the y-axis represents distance.

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How do you interpret the slope of a distance-time graph?

Back

The slope of a distance-time graph represents the speed or velocity of the object; a steeper slope indicates a higher speed.

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What does a horizontal line on a distance-time graph indicate?

Back

A horizontal line indicates that the object is at rest, as there is no change in distance over time.

Front

How do you find the total distance traveled from a distance-time graph?

Back

To find the total distance traveled, calculate the vertical distance covered in each segment of the graph and sum them up.

Front

What is the significance of a break in a piecewise function's graph?

Back

A break in a piecewise function's graph indicates a discontinuity, where the function does not have a defined value at that point.