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 intervals of its domain.

Front

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

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and use the corresponding expression to find the function value.

Front

What does it mean if a piecewise function has a value that 'does not exist'?

Back

It means that there is no defined output for that input value within the function's defined intervals.

Front

What is the significance of the graph of a piecewise function?

Back

The graph visually represents the different expressions of the function over their respective intervals, showing how the function behaves at different points.

Front

If f(x) = { x^2 for x < 0; 2x for x >= 0, what is f(-2)?

Back

f(-2) = (-2)^2 = 4.

Front

If f(x) = { 3 for x < 1; x + 2 for x >= 1, what is f(1)?

Back

f(1) = 1 + 2 = 3.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x) for which the function is defined.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (f(x)) that the function can produce.

Front

How can you determine continuity in a piecewise function?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph at the points where the pieces connect.

Front

What is a jump discontinuity in a piecewise function?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit at a point do not equal each other, resulting in a 'jump' in the graph.