Evaluating 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's value.

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

Evaluate m(4) if m(x) = { 0 for x < 2; 1 for 2 ≤ x < 5; -3 for x ≥ 5 }

Back

m(4) = 1.

Front

Evaluate f(2) if f(x) = { -2 for x < 1; 1 for 1 ≤ x < 3; 4 for x ≥ 3 }

Back

f(2) = 1.

Front

Evaluate m(-3) if m(x) = { 3 for x < -2; -3 for -2 ≤ x < 0; 0 for x ≥ 0 }

Back

m(-3) = 3.

Front

Evaluate f(1) if f(x) = { -2 for x < 1; 6 for 1 ≤ x < 2; 4 for x ≥ 2 }

Back

f(1) = -2.

Front

What does it mean for a function to be undefined at a point?

Back

A function is undefined at a point if there is no corresponding output value for that input in the function's definition.

Front

What is the significance of the brackets in interval notation?

Back

Brackets [ ] indicate that the endpoint is included in the interval, while parentheses ( ) indicate that the endpoint is not included.