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.

Front

How do you determine the domain of a piecewise function?

Back

To determine the domain, identify the intervals for which each piece of the function is defined and combine them.

Front

What does the notation f(x) mean in a piecewise function?

Back

f(x) represents the output of the function for a given input x, which may depend on which piece of the function is applicable.

Front

What is the significance of domain restrictions in piecewise functions?

Back

Domain restrictions specify the values of x for which each piece of the function is valid, ensuring the function is well-defined.

Front

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

Back

To evaluate, determine which piece of the function applies to the given input and use that expression to find the output.

Front

What is the graphical representation of a piecewise function?

Back

A piecewise function is represented graphically by different line segments or curves, each corresponding to a specific interval of the domain.

Front

What is the difference between continuous and discontinuous piecewise functions?

Back

Continuous piecewise functions have no breaks in their graphs, while discontinuous piecewise functions have jumps or gaps.

Front

How can you identify the equation of a piece of a piecewise function from its graph?

Back

You can identify the equation by observing the slope and intercept of the line segment or curve in the relevant interval.

Front

What is the output of f(-3) if f(x) = { x + 1, x < -2; 2x, -2 ≤ x ≤ 1; x - 3, x > 1 }?

Back

f(-3) = -3.

Front

What is the output of f(0) if f(x) = { x + 1, x < -2; 2x, -2 ≤ x ≤ 1; x - 3, x > 1 }?

Back

f(0) = 4.