Step Functions Practice

Front

What is a step function?

Back

A step function is a piecewise constant function that jumps from one value to another without taking on any values in between.

Front

What is the greatest integer function?

Back

The greatest integer function, denoted as [[x]], returns the largest integer less than or equal to x.

Front

How do you evaluate a step function at a given point?

Back

To evaluate a step function at a point, determine which interval the point falls into and use the corresponding constant value.

Front

What is the value of f(x) = 2[[x-3.5]] when x = 2?

Back

f(2) = 2[[-1.5]] = 2*(-2) = -4.

Front

If f(x) = 2[[x-3.5]], what is f(3.5)?

Back

f(3.5) = 2[[0]] = 2*0 = 0.

Front

What is the cost of mailing a package that weighs 2.1 ounces if the cost is based on weight?

Back

The cost for mailing a package that weighs 2.1 ounces is 41 cents.

Front

How do you calculate the total cost of multiple items with tax?

Back

Multiply the price of each item by the quantity, then add the tax to find the total cost.

Front

What is the total cost for three candy bars at $0.55 each with tax included?

Back

Total cost = 3 * $0.55 + tax = $1.74.

Front

What is the value of y when x = -2 in the equation y = x^2?

Back

When x = -2, y = (-2)^2 = 4.

Front

What is the difference between a linear function and a step function?

Back

A linear function has a constant rate of change, while a step function has constant values over intervals with jumps between them.