Piece-Wise Functions Practice

Front

What is a piece-wise function?

Back

A piece-wise function is a function that is defined by different expressions or formulas for different intervals of the input variable.

Front

How do you evaluate a piece-wise function?

Back

To evaluate a piece-wise function, determine which interval the input value falls into and then use the corresponding expression to find the output.

Front

What does the notation f(x) mean in piece-wise functions?

Back

f(x) represents the output of the function for a given input x.

Front

What is the significance of the domain in piece-wise functions?

Back

The domain specifies the input values for which the function is defined, often divided into intervals for different expressions.

Front

How do you graph a piece-wise function?

Back

To graph a piece-wise function, plot each segment according to its defined interval and ensure to use open or closed circles to indicate whether endpoints are included.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

Front

Evaluate f(2) for the piece-wise function: f(x) = { 3x - 6, 3 ≤ x < 6; 0, x < 3 }

Back

f(2) = 0, since 2 is less than 3.

Front

Evaluate f(4) for the piece-wise function: f(x) = { 3x - 6, 3 ≤ x < 6; 0, x < 3 }

Back

f(4) = 3(4) - 6 = 6.

Front

What is the output of f(0) for the piece-wise function: f(x) = { 3x - 6, 3 ≤ x < 6; -3, x < 3 }

Back

f(0) = -3, since 0 is less than 3.

Front

If Mrs. MacIntyre earns $15 per hour, how much does she make for 45 hours?

Back

Mrs. MacIntyre makes $15 * 45 = $675.