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 use the corresponding expression to find the function's value.

Front

What is the value of f(-3) if f(x) = { -3 for x < -2, 1 for -2 ≤ x < 1, 3 for x ≥ 1 }?

Back

-3

Front

What is the cost for a group of 20 people to enter a park if the entry fee is $60 for the first 10 people and $50 for each additional person?

Back

$1200

Front

How do you calculate the total earnings of a painter who charges different rates for different hours worked?

Back

Calculate the earnings for each segment of hours worked at the respective rates and sum them up.

Front

If a painter charges $12 per hour for the first 40 hours, $18 for the next 10 hours, and $24 for hours beyond that, how much does he earn for 70 hours?

Back

$1140

Front

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

Back

4

Front

What is the value of f(1) if f(x) = { 6 for x < 0, -2 for 0 ≤ x < 2, sqrt(2) for x ≥ 2 }?

Back

-2

Front

What does it mean for a function to be undefined at a certain point?

Back

A function is undefined at a certain point if there is no valid output for that input, often due to division by zero or other restrictions.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each segment of the function according to its defined intervals, ensuring to use open or closed circles as appropriate.