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?

Back

To evaluate a piecewise function, identify the interval that the input value falls into and use the corresponding expression to find the output.

Front

What is the formula for calculating earnings in a piecewise function scenario?

Back

Earnings = (Hourly Rate for first interval * Hours in first interval) + (Hourly Rate for second interval * Hours in second interval) + (Hourly Rate for third interval * Hours in third interval) if applicable.

Front

If a painter works 50 hours, how do you calculate his earnings?

Back

Earnings = (12 * 40) + (18 * 10) = $480 + $180 = $660.

Front

What is f(-5) if f(x) = {0, x < -3; 2, -3 ≤ x < 1; 5, x ≥ 1}?

Back

f(-5) = 0.

Front

What is g(7) if g(x) = {x - 10, x < 0; 2x + 3, 0 ≤ x < 10; 3x - 5, x ≥ 10}?

Back

g(7) = 2(7) + 3 = 17.

Front

Using a graph, how do you find f(-3)?

Back

Locate -3 on the x-axis, then find the corresponding y-value on the graph.

Front

What is f(2) if f(x) = {0, x < 1; 1, 1 ≤ x < 3; 3, x ≥ 3}?

Back

f(2) = 1.

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

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (y-values) that the function can produce.