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 calculate earnings using a piecewise function?

Back

To calculate earnings, identify the intervals of hours worked and apply the corresponding rates for each interval.

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 would you express this as a piecewise function?

Back

E(x) = { 12x for 0 ≤ x ≤ 40; 480 + 18(x - 40) for 40 < x ≤ 50; 480 + 180 + 24(x - 50) for x > 50 }.

Front

What is the domain of a function?

Back

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

Front

In the context of flow rates, what does a domain restriction of x ≥ 0 imply?

Back

It implies that the flow rate is only defined for non-negative values of x, meaning the flow cannot be negative.

Front

How can you determine the number of distinct temperature ranges in a piecewise function graph?

Back

Count the number of separate intervals on the graph where the temperature is defined by different expressions.

Front

What does the interval -2 < x ≤ 1 represent in a piecewise function?

Back

It represents the time period during which the growth of the plant is being tracked, starting just after -2 and up to 1.

Front

What is the significance of the endpoints in a piecewise function?

Back

Endpoints determine whether the values at those points are included or excluded in the function's domain.

Front

How do you match a graph with its corresponding equation?

Back

Analyze the key features of the graph (like slopes, intercepts, and intervals) and compare them to the characteristics of the equations.

Front

What is a continuous piecewise function?

Back

A continuous piecewise function is one where there are no breaks or jumps in the graph, meaning the function values connect at the endpoints.