Using functions in models and decision making step and piecewise functions sheet 11 answers 2026

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Given a piecewise function, sketch a graph. Indicate on the x-axis the boundaries defined by the intervals on each piece of the domain. For each piece of the domain, graph on that interval using the corresponding equation pertaining to that piece.
A step function (or staircase function) is a piecewise function containing all constant pieces. The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next.
Here are the steps to graph a piecewise function. Step 1: First, understand what each definition of a function represents. Step 2: Write the intervals shown in the function definition along with their definitions. Step 3: Create a two-column table labeled \(x\) and \(y\) corresponding to each interval.

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We use piecewise functions to describe situations in which a rule or relationship changes as the input value crosses certain boundaries. For example, we often encounter situations in business for which the cost per piece of a certain item is discounted once the number ordered exceeds a certain value.
A piecewise function exists when a function is defined by two or more different functions throughout its domain. The first step in evaluating a piecewise function is to determine which function definition applies depending on the value of x that is being input.
To evaluate a piecewise function, follow these steps: Determine in which interval does the given value for x lies. Subtitute that value on its corresponding function. Evaluate the expression.

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