Linear Piecewise Functions - Harvey

Front

What is a linear piecewise function?

Back

A function that is defined by different expressions or formulas over different intervals of its domain.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How do you determine the domain of a piecewise function?

Back

Identify the intervals for which each piece of the function is defined and combine them.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

What is the difference between open and closed intervals?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

How do you find the value of a piecewise function at a specific point?

Back

Determine which piece of the function applies to that point and use the corresponding formula.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; it shows how much y changes for a unit change in x.

Front

What is a quadratic function?

Back

A function that can be expressed in the form y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point on the graph of the function, depending on its orientation.