Exploring Piecewise Functions and Their Applications

The video tutorial introduces piecewise functions, explaining that they are functions defined by different rules over different parts of their domain. It provides an example of a piecewise function and demonstrates how to graph it, highlighting the importance of understanding inequalities in the function's definition. The tutorial also discusses the absolute value function as a piecewise function, showing how it changes based on the input value. The video concludes with a call to action for viewers to engage with the content and subscribe for more lessons.

What is a piecewise function?

• A function defined by a single rule.

• A function defined in pieces.

• A function that only takes positive values.

• A function that is always continuous.

In a simple function like f(x) = 2x, what happens to the input value?

• It is divided by 2.

• It is squared.

• It is multiplied by 2.

• It is subtracted by 2.

When graphing the piecewise function, what is the rule for x ≤ 0?

• f(x) = -x

• f(x) = 3

• f(x) = x

• f(x) = 2x

What is the value of f(-2) for the piecewise function where f(x) = 2x for x ≤ 0?

• 4

• -4

• -2

• 2

For x > 0, what is the value of the piecewise function in the example?

• 0

• 2x

• x

• 3

How is a discontinuity at x = 0 indicated in the graph?

• With an empty circle.

• With a filled circle.

• With a square.

• With a dashed line.

What does the absolute value function do to a negative input?

• It adds 1 to the input.

• It flips the sign of the input.

• It squares the input.

• It subtracts 1 from the input.

What is the output of the absolute value function for an input of -3?

• -3

• 1

• 0

• 3

What is the output of the absolute value function for an input of 4?

• 1

• 0

• -4

• 4

What happens to the graph of the absolute value function at x = 0?

• It becomes undefined.

• It changes slope.

• It continues as a straight line.

• It jumps to a different value.