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 evaluate a piecewise function at a specific point?

Back

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

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined, often specified by the intervals in the piecewise definition.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (y-values) that the function can produce, based on the defined pieces.

Front

Evaluate f(0) for the piecewise function: f(x) = { 2x + 4, x < 0; x^2 - 1, x >= 0 }

Back

f(0) = 0^2 - 1 = -1.

Front

Evaluate g(-2) for the piecewise function: g(x) = { x + 5, x < -1; 2x - 1, x >= -1 }

Back

g(-2) = -2 + 5 = 3.

Front

Evaluate f(-3) for the piecewise function: f(x) = { -x - 1, x < -1; x + 2, x >= -1 }

Back

f(-3) = -(-3) - 1 = 2.

Front

Evaluate f(6) for the piecewise function: f(x) = { 3x - 5, x < 5; x + 1, x >= 5 }

Back

f(6) = 6 + 1 = 7.

Front

Find f(-2) for the piecewise function: f(x) = { x^2 - 4, x < -1; 2x + 2, x >= -1 }

Back

f(-2) = (-2)^2 - 4 = 0.

Front

What is the importance of continuity in piecewise functions?

Back

Continuity in piecewise functions ensures that there are no jumps or breaks in the graph, which is important for certain applications in calculus and real-world modeling.