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 value of a piecewise function at a specific point?

Back

To determine the value of a piecewise function at a specific point, identify which piece of the function applies to that point based on its domain restrictions.

Front

What does the domain of a function represent?

Back

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

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

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

Back

f(-1) = -1 + 2 = 1.

Front

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

Back

The graph of a piecewise function visually represents how the function behaves over different intervals of its domain.

Front

How can you identify the domain restrictions of a piecewise function from its graph?

Back

You can identify domain restrictions by observing the x-values where each piece of the function is defined and any breaks or holes in the graph.

Front

What is the value of f(2) if f(x) = { 2x for x < 2; x^2 for x ≥ 2 }?

Back

f(2) = 2^2 = 4.

Front

What does it mean if a piecewise function has a closed dot at a point on its graph?

Back

A closed dot indicates that the function includes that point in its domain (the value is defined at that point).

Front

What does it mean if a piecewise function has an open dot at a point on its graph?

Back

An open dot indicates that the function does not include that point in its domain (the value is not defined at that point).