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 determine the domain of a piecewise function?

Back

The domain of a piecewise function is determined by the intervals for which each piece of the function is defined.

Front

What does 'DNE' stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function value is not defined for a given input.

Front

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

Back

To evaluate a piecewise function at a specific point, identify which interval the point falls into and use the corresponding expression.

Front

What is the significance of the domain restriction in piecewise functions?

Back

Domain restrictions indicate the values of x for which the function is defined, ensuring that the function behaves correctly within those intervals.

Front

If f(x) = { x^2 for x < 0; 3x + 1 for x ≥ 0 }, what is f(-2)?

Back

f(-2) = 4, since -2 falls in the interval x < 0.

Front

If f(x) = { 2x - 1 for x < 1; x^2 for x ≥ 1 }, what is f(4)?

Back

f(4) = 16, since 4 falls in the interval x ≥ 1.

Front

What is the graphical representation of a piecewise function?

Back

The graphical representation of a piecewise function consists of multiple segments, each corresponding to a different piece of the function, often with breaks or jumps at the boundaries.

Front

How can you find the value of g(7) if g(x) = { 2x - 3 for x < 5; x + 10 for x ≥ 5 }?

Back

g(7) = 17, since 7 falls in the interval x ≥ 5.

Front

What is the importance of continuity in piecewise functions?

Back

Continuity in piecewise functions ensures that there are no jumps or breaks in the function at the boundaries of the pieces.