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 then use the corresponding expression for that interval.

Front

What is the value of f(-2) if f(x) = { 4, x < 0; 3, x >= 0 }?

Back

The value of f(-2) is 4, since -2 is less than 0.

Front

What is the value of f(0) if f(x) = { 4, x < 0; 3, x >= 0 }?

Back

The value of f(0) is 3, since 0 is greater than or equal to 0.

Front

How do 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 circles to indicate whether endpoints are included.

Front

What does f(-3) represent in a piecewise function?

Back

f(-3) represents the output of the function when the input x is -3, determined by the appropriate piece of the function for that interval.

Front

What is the equation for f(x) when x is less than or equal to 2 in the function f(x) = { |x|, x <= 2; 3, x > 2 }?

Back

The equation for f(x) when x is less than or equal to 2 is f(x) = |x|.

Front

What is the significance of using absolute value in piecewise functions?

Back

Using absolute value in piecewise functions allows for the definition of a function that outputs non-negative values, regardless of the input's sign.

Front

How can you determine the continuity of a piecewise function at a boundary point?

Back

To determine continuity at a boundary point, check if the left-hand limit and right-hand limit at that point are equal and if the function value at that point matches these limits.

Front

What is the value of f(4) if f(x) = { 4, x < 0; 3, x >= 0 }?

Back

The value of f(4) is 3, since 4 is greater than or equal to 0.