Graphing 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 graph a piecewise function?

Back

To graph a piecewise function, identify the intervals for each piece, graph each piece according to its formula, and ensure to use open or closed dots based on whether the endpoints are included.

Front

What does the notation f(x) = { x if x < 4; -x+1 if x ≥ 4 mean?

Back

This notation means that for values of x less than 4, the function f(x) equals x, and for values of x greater than or equal to 4, f(x) equals -x + 1.

Front

What is the importance of endpoints in piecewise functions?

Back

Endpoints determine whether the function includes or excludes certain values, affecting the graph's continuity and the function's behavior at those points.

Front

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

Back

To determine the value, identify which interval the point falls into and use the corresponding expression to calculate the function's value.

Front

What is the difference between open and closed intervals in piecewise functions?

Back

Open intervals do not include the endpoint values (denoted with parentheses), while closed intervals do include the endpoint values (denoted with brackets).

Front

What is the graphical representation of f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

The graph consists of a line with a negative slope for x < 4 and a line with a positive slope starting from the point (4, 4) for x ≥ 4.

Front

How can you identify a piecewise function from a graph?

Back

Look for distinct segments or lines that change direction or slope at certain x-values, indicating different expressions for different intervals.

Front

What is the significance of the slope in piecewise linear functions?

Back

The slope indicates the rate of change of the function in each interval; different slopes can show different behaviors of the function.

Front

How do you match a graph to its piecewise function?

Back

Analyze the graph's segments, identify the slopes and intercepts, and compare them to the expressions in the piecewise function to find a match.