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 does it mean if a piecewise function is undefined at a certain point?

Back

A piecewise function is undefined at a certain point if there is no expression defined for that point in the function's definition.

Front

Evaluate the piecewise function: f(x) = { x^2 for x < 0; 2x + 1 for x >= 0 } at x = -3.

Back

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

Front

Evaluate the piecewise function: f(x) = { x + 2 for x < 1; 3 for x = 1; x^2 for x > 1 } at x = 1.

Back

f(1) = 3.

Front

What is the cost function for buying cupcakes if the first 10 cost $2 each and any additional cost $1.50 each?

Back

C(x) = { 2x for 0 < x <= 10; 20 + 1.5(x - 10) for x > 10 }.

Front

If a dog weighs 50 pounds, how much do you need to pay if the cost is $1.50 per pound for the first 40 pounds and $2 for each additional pound?

Back

Cost = 40 * 1.50 + (50 - 40) * 2 = 60 + 20 = $80.

Front

Evaluate the piecewise function: f(x) = { -x for x < 0; x^2 for 0 <= x <= 2; 4 for x > 2 } at x = 3.

Back

f(3) = 4.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined.

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.