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 value is undefined at a certain point.

Front

What is the significance of the domain in piecewise functions?

Back

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

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed dots as appropriate.

Front

What is the value of g(4) if g(x) = { -x - 1 for x < 0; 2x - 1 for x >= 0 }?

Back

g(4) = 2(4) - 1 = 7.

Front

What is the value of h(5) if h(x) = { x^2 for x < 0; 10 - x for x >= 0 }?

Back

h(5) = 10 - 5 = 5.

Front

What is the value of f(-2) if f(x) = { 2x + 8 for x < -1; x^2 for -1 <= x < 2; 3 for x >= 2 }?

Back

f(-2) = 2(-2) + 8 = 4.

Front

What is the value of g(7) if g(x) = { -3x + 2 for x < 0; x^2 - 4 for 0 <= x < 5; 2x + 1 for x >= 5 }?

Back

g(7) = 2(7) + 1 = 15.

Front

What is the purpose of matching graphs with equations in piecewise functions?

Back

Matching graphs with equations helps to visually understand how the function behaves across different intervals.