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 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 that there is no value assigned to that point in the function's definition.

Front

Evaluate f(4) if f(x) = { -1 for x < 2, 5 for 2 ≤ x < 5, 3 for x ≥ 5 }

Back

f(4) = 5.

Front

Evaluate f(-1) if f(x) = { 2 for x < 0, 3 for 0 ≤ x < 2, 5 for x ≥ 2 }

Back

f(-1) = 2.

Front

What is the value of f(2) if f(x) = { -1 for x < 2, 5 for x = 2, 2 for x > 2 }

Back

f(2) = 5.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

Front

Evaluate k(3) if k(x) = { 0 for x < 1, 6 for 1 ≤ x < 4, 10 for x ≥ 4 }

Back

k(3) = 6.

Front

What is the significance of open and closed intervals in piecewise functions?

Back

Open intervals indicate that the endpoint is not included in the function's value, while closed intervals indicate that the endpoint is included.

Front

Evaluate f(-1) if f(x) = { 3 for x < 0, 2 for x = 0, 1 for x > 0 }

Back

f(-1) = 3.