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

What does the DOMAIN of a function refer to?

Back

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

Front

What does the RANGE of a function refer to?

Back

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

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 is the significance of domain restrictions in piecewise functions?

Back

Domain restrictions indicate the specific values of x for which a particular piece of the function applies.

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 corresponds to that input value and use the appropriate formula.

Front

What is the value of f(0) if f(x) = { 2x + 4 for x < 1; x^2 for x ≥ 1 }?

Back

f(0) = 2(0) + 4 = 4.

Front

What is the value of f(2) if f(x) = { 2x + 4 for x < 1; x^2 for x ≥ 1 }?

Back

f(2) = 2^2 = 4.

Front

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

Back

f(1) = 3(1) = 3.

Front

What is the graphical representation of a piecewise function?

Back

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