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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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

• f(x) = -x

• f(x) = 3

• f(x) = x

• f(x) = 2x

Tags

CCSS.HSF-IF.C.7B

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

• 4

• -4

• -2

• 2

Tags

CCSS.HSF.IF.A.2

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

• 0

• 2x

• x

• 3

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7D

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

• -3

• 1

• 0

• 3

Tags

CCSS.HSF.IF.A.2

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

• 1

• 0

• -4

• 4

Tags

CCSS.HSF.IF.A.2

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.