Understanding Piecewise Functions and Absolute Values

This video tutorial covers evaluating, graphing, and writing piecewise functions, including step and absolute value functions. It provides examples of evaluating piecewise functions, graphing them, and writing them from graphs. The tutorial also explains step functions and demonstrates how to write and graph them. Finally, it covers writing absolute value functions and converting them into piecewise functions.

What is a piecewise function?

• A function defined by a single equation.

• A function defined by two or more equations, each applying to a different part of its domain.

• A function that is always linear.

• A function that only applies to positive numbers.

In the example f(x) = x - 2 if x ≤ 0 and 2x + 1 if x > 0, what is f(0)?

• 2

• 1

• -2

• 0

How do you determine which part of a piecewise function to use for a given x value?

• Use the part with the highest slope.

• Use the part that includes the x value in its domain.

• Use the part with the lowest y-intercept.

• Use the part that is defined for all x.

What is the domain of the piecewise function y = -x - 4 if x < 0 and y = x if x ≥ 0?

• All real numbers

• Only zero

• All negative numbers

• All positive numbers

What is the range of the piecewise function y = -x - 4 if x < 0 and y = x if x ≥ 0?

• y is equal to -4

• y is greater than -4

• y is greater than or equal to 0

• y is less than -4

How do you write a piecewise function from a graph?

• Ignore the domain restrictions.

• Identify the y-intercepts only.

• Determine the slope and y-intercept for each line segment.

• Use only the x-intercepts.

What is a step function?

• A function that only increases.

• A piecewise function defined by constant values over each part of its domain.

• A function that only decreases.

• A function with a continuous curve.

In the karaoke machine example, what is the cost for renting the machine for 3 days?

• $150

• $125

• $100

• $75

How can an absolute value function be expressed?

• As a piecewise function.

• As a quadratic function.

• As a constant function.

• As a single linear equation.

What is the vertex of the absolute value function in the holography example?

• (1, 1)

• (8, 5)

• (5, 8)

• (0, 0)