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 corresponding output value for that input in the function's definition.

Front

Given f(x) = { x + 2, x < 0; 3, x = 0; x^2, x > 0 }, what is f(-1)?

Back

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

Front

Given g(x) = { 5, x < 1; x - 1, 1 ≤ x < 3; 10, x ≥ 3 }, what is g(2)?

Back

g(2) = 2 - 1 = 1.

Front

What is the value of f(0) if f(x) = { 2x, x < 0; 3, x = 0; x + 1, x > 0 }?

Back

f(0) = 3.

Front

How do you find the value of a piecewise function at a boundary point?

Back

At a boundary point, check the definition of the function at that point to see which expression applies.

Front

Evaluate k(3) if k(x) = { x^2, x < 2; 6, x = 2; 2x, x > 2 }.

Back

k(3) = 2 * 3 = 6.

Front

If h(x) = { -x, x < 0; 7, x = 0; x^2, x > 0 }, what is h(5)?

Back

h(5) = 5^2 = 25.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function defines the intervals over which each piece of the function is applicable.