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 the input variable.

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 formula for the piecewise function f(x) = { 2x + 1 if x < 3; x - 1 if x >= 3 }?

Back

This function has two parts: for x < 3, use 2x + 1; for x >= 3, use x - 1.

Front

Evaluate f(2) for the piecewise function f(x) = { 2x + 1 if x < 3; x - 1 if x >= 3 }.

Back

f(2) = 2(2) + 1 = 5.

Front

Evaluate f(4) for the piecewise function f(x) = { 2x + 1 if x < 3; x - 1 if x >= 3 }.

Back

f(4) = 4 - 1 = 3.

Front

What is the importance of the domain in piecewise functions?

Back

The domain determines the intervals for which each piece of the function is applicable, affecting how the function behaves.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece on its respective interval and ensure to use open or closed circles to indicate whether endpoints are included.

Front

What does it mean if a piecewise function has a jump discontinuity?

Back

A jump discontinuity occurs when the function has different values at a certain point from the left and right, indicating a 'jump' in the graph.

Front

Evaluate f(5) for the piecewise function f(x) = { x^2 if x < 3; 2x if x >= 3 }.

Back

f(5) = 2(5) = 10.

Front

What is the output of f(0) for the piecewise function f(x) = { x + 2 if x < 1; 3x if x >= 1 }?

Back

f(0) = 0 + 2 = 2.