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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF.IF.A.2