Transforming Functions in Algebra

This video tutorial covers piecewise functions, explaining their definition and characteristics. It includes examples of graphing piecewise functions with different components, such as linear, absolute value, square root, cube root, and exponential functions. The tutorial also discusses how to determine the domain, range, and end behavior of these functions.

What is a piecewise function?

• A function defined by multiple sub-functions, each applying to a certain interval.

• A function that has no domain.

• A function that is always linear.

• A function defined by a single equation.

Which of the following can be considered a piecewise function?

• y = x^2

• y = sin(x)

• y = |x|

• y = 2x + 3

When graphing piecewise functions, what should you consider for each sub-function?

• The number of pencils used.

• The interval of the main function's domain.

• The type of paper used.

• The color of the graph.

How do you determine if a point is an open or closed circle on a graph?

• By the color of the point.

• By the interval notation (less than or equal to, or greater than).

• By the size of the point.

• By the shape of the point.

What is the domain of the function f(x) = x + 3 for x ≤ 1 and f(x) = -2x for x > 1?

• x ≤ 1

• All real numbers.

• All real numbers except 1.

• x > 1

What is the range of the function f(x) = x + 3 for x ≤ 1 and f(x) = -2x for x > 1?

• y < 4

• y ≥ 4

• y ≤ 4

• y = 4

For the function with an absolute value and a square root function, what is the domain?

• All real numbers.

• All real numbers except x = -5.

• x > -5

• x < -5

For the function with an absolute value and a square root function, what is the range?

• y = 0 and y = 4

• y > 0 and y < 4

• All real numbers.

• y < 0 and y > 4

What is the maximum y-value for the function with three sub-functions?

• 3

• 2

• 1

• 4

What is the domain of the function with three sub-functions?

• x < 1

• x > 1

• All real numbers.

• All real numbers except x = 1.