Piecewise and Composite Functions

The video tutorial covers piecewise functions, including graphing techniques and domain/range analysis. It explores quadratic and linear functions within piecewise contexts and delves into function composition with practical examples. The session concludes with details on homework assignments and due dates.

What is a piecewise function?

• A function that is always continuous.

• A function that has no domain restrictions.

• A function defined by multiple equations over different intervals.

• A function defined by a single equation.

How should the graph of f(x) = x^2 for x < 0 be represented?

• With an open circle at x = 0.

• With a closed circle at x = 0.

• With a solid line for x < 0.

• With a dashed line for x < 0.

What is the slope of the line for f(x) = x in the interval 0 ≤ x < 1?

• 2

• -1

• 1

• 0

For f(x) = x + 2, what is the value of f(1)?

• 4

• 1

• 2

• 3

What does it mean for a function to be discontinuous?

• The function has no range.

• The function has breaks or jumps.

• The function has no domain.

• The function is defined by a single equation.

What is the domain of the piecewise function discussed?

• From negative infinity to positive infinity

• From 0 to 2

• From 1 to 3

• From -1 to 1

What is the range of the piecewise function discussed?

• From negative infinity to positive infinity

• From 1 to 3

• From -1 to 1

• From 0 to infinity

What is the value of f(0) for the function f(x) = x - 2 when x < 1?

• 2

• -2

• 0

• -1

How is the point at x = 1 represented for the function f(x) = √x?

• With a solid line

• With a dashed line

• With an open circle

• With a closed circle

What is the value of f(4) for the function f(x) = 3?

• 1

• 2

• 3

• 4