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 then 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 output value for that input, often due to the input not falling within any defined interval.

Front

Given f(x) = { x^2 for x < 0, 2x + 1 for x >= 0 }, evaluate f(-3).

Back

f(-3) = (-3)^2 = 9.

Front

Given f(x) = { x^2 for x < 0, 2x + 1 for x >= 0 }, evaluate f(2).

Back

f(2) = 2(2) + 1 = 5.

Front

What is the importance 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, determining where the function can be evaluated.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots to indicate whether endpoints are included.

Front

What is the output of a piecewise function if the input is not in any defined interval?

Back

The output is undefined if the input does not fall within any defined interval of the piecewise function.

Front

Given the graph of f(x), how do you find f(-4)?

Back

Locate -4 on the x-axis, then find the corresponding y-value on the graph.

Front

If f(x) is defined as f(x) = { 3 for x < 1, 5 for x = 1, 7 for x > 1 }, what is f(1)?

Back

f(1) = 5.