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 'DNE' stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function value is not defined for a given input.

Front

What is the value of f(2) if f(x) = -x + 4 for x < 2 and f(x) = 2x - 6 for x ≥ 2?

Back

f(2) = 2(2) - 6 = -2.

Front

What is the range of a piecewise function?

Back

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

Front

How do you graph a piecewise function?

Back

Graph each piece of the function on its respective interval, using open or closed dots to indicate whether endpoints are included.

Front

What is the significance of the 'if' statement in piecewise functions?

Back

The 'if' statement specifies the conditions under which each piece of the function applies.

Front

What is the value of g(7) if g(x) = -x + 10 for x < 5 and g(x) = 2x - 6 for x ≥ 5?

Back

g(7) = 2(7) - 6 = 8.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

How can you find the output of a piecewise function for a given input?

Back

Identify which piece of the function corresponds to the input value and use that expression to calculate the output.