4.5 Graphing Piecewise Functions (8A)

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 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 based on its domain restrictions, and then use that expression to find the value.

Front

What does the notation -2 < x ≤ 1 mean?

Back

This notation indicates that x is greater than -2 and less than or equal to 1.

Front

What is the domain of a function?

Back

The domain of a function is the set of all 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

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its domain restrictions, ensuring to use open or closed dots as appropriate for endpoints.

Front

What is the significance of endpoints in piecewise functions?

Back

Endpoints indicate whether a value is included in the domain of a piece (closed dot) or excluded (open dot).

Front

Evaluate f(-1) for the piecewise function defined as: f(x) = { x + 1 for x < 0; 2x for x ≥ 0 }

Back

f(-1) = -1 + 1 = 0.

Front

Evaluate f(-4) for the piecewise function defined as: f(x) = { x + 2 for x < -2; -3 for -2 ≤ x < 1; x - 1 for x ≥ 1 }

Back

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

Front

What is a graph of a piecewise function?

Back

A graph of a piecewise function consists of multiple segments, each representing a different expression of the function over its specific domain.