Intro to Piecewise Functions

Front

What is a piecewise function?

Back

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

Front

What does the Vertical Line Test determine?

Back

The Vertical Line Test determines if a graph represents a function. If any vertical line intersects the graph more than once, it is not a function.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, identify which interval the point falls into and use the corresponding expression to find the function's value.

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

What is the range of a function?

Back

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

Front

How do you express the domain of a piecewise function?

Back

The domain of a piecewise function can be expressed using interval notation, indicating the intervals for which each piece of the function is valid.

Front

What is the significance of open and closed intervals in domain and range?

Back

Open intervals (e.g., (a, b)) do not include their endpoints, while closed intervals (e.g., [a, b]) do include their endpoints.

Front

Evaluate f(6) for the piecewise function: f(x) = { 3, if x < 0; 1, if 0 ≤ x < 5; 3, if x ≥ 5 }

Back

f(6) = 3.

Front

What is the range of the function f(x) = { x^2, if x < 0; 2x + 1, if 0 ≤ x < 3; 5, if x ≥ 3 }?

Back

The range is [0, 5].

Front

Given the piecewise function f(x) = { -x, if x < 0; x^2, if 0 ≤ x < 2; 3, if x ≥ 2 }, find f(2).

Back

f(2) = 3.