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 does it mean if a piecewise function is undefined at a certain point?

Back

If a piecewise function is undefined at a certain point, it means there is no output value for that input, often due to the input not falling within any defined interval.

Front

Evaluate f(0) for the piecewise function: f(x) = { 4 if x < 1; undefined if x = 1; 2 if x > 1 }

Back

f(0) = 4.

Front

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

Back

f(2) = 1.

Front

Using the graph of a piecewise function, how do you find f(-3)?

Back

Locate -3 on the x-axis, find the corresponding y-value from the graph.

Front

Evaluate f(1) for the piecewise function: f(x) = { undefined if x < 1; 1 if x = 1; 2 if x > 1 }

Back

f(1) = 1.

Front

Evaluate f(-4) for the piecewise function: f(x) = { 2 if x < -2; undefined if -2 ≤ x ≤ 0; 3 if x > 0 }

Back

f(-4) = 2.

Front

What is the domain of a piecewise function?

Back

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

Front

What is the range of a piecewise function?

Back

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