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 'DNE' stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function does not have a value at a certain point.

Front

If g(x) = { 2x + 1 for x < 0; 3x - 5 for x >= 0, what is g(7)?

Back

g(7) = 3(7) - 5 = 21 - 5 = 16.

Front

What is the value of g(-2) if g(x) = { x^2 - 1 for x < 0; 2x + 3 for x >= 0?

Back

g(-2) = (-2)^2 - 1 = 4 - 1 = 3.

Front

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

Back

To find the limit of a piecewise function at a point, evaluate the function from both sides of the point and check if the limits are equal.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the intervals for which each piece of the function is valid.

Front

Evaluate f(-2) if f(x) = { x + 6 for x < 0; 2x for x >= 0.

Back

f(-2) = -2 + 6 = 4.

Front

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

Back

f(-3) = -(-3) - 1 = 3 - 1 = 2.

Front

If h(x) = { x^2 for x < 0; 3 for x >= 0, what is h(5)?

Back

h(5) = 3.