Evaluating a Piecewise Function

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 f(-3) represent in a piecewise function?

Back

f(-3) represents the value of the function at x = -3, determined by the appropriate piece of the function defined for that interval.

Front

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

Back

m(-3) = 2(-3) + 1 = -6 + 1 = -5.

Front

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

Back

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

Front

What is the significance of the domain in a piecewise function?

Back

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

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

What is the value of f(6) if f(x) = { 2x for x < 5; x - 3 for x >= 5 }?

Back

f(6) = 6 - 3 = 3.

Front

What does it mean if a piecewise function has a discontinuity?

Back

A discontinuity in a piecewise function means there is a jump or break in the graph, indicating that the function is not continuous at that point.

Front

If m(x) = { x + 2 for x < 1; 4 for x = 1; x^2 for x > 1 }, what is m(1)?

Back

m(1) = 4.