Understanding and Graphing Piecewise Functions

The video tutorial covers interpreting and graphing piecewise functions, highlighting their real-life applications in cell phone billing and shipping rates. It provides examples using a Sprint calling plan and demonstrates how to graph piecewise functions with two and three pieces, including using a graphing calculator.

What is a real-life application of piecewise functions?

• Finding the slope of a line

• Solving quadratic equations

• Determining cell phone billing rates

• Calculating the area of a circle

In the 2005 Sprint cell phone plan, what is the monthly bill for using 360 minutes?

• $40

• $60

• $50

• $30

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CCSS.6.EE.B.7

If a customer's bill is $55, how many minutes could they have used?

• 640 minutes

• 360 minutes

• 700 minutes

• 600 minutes

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CCSS.HSF-IF.C.7D

What does a closed point on a graph indicate?

• The graph has a horizontal asymptote

• The graph has a vertical asymptote

• The function is defined at that point

• The function is not defined at that point

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CCSS.HSF-IF.C.7B

How is the function G(x) = 2 defined for x ≥ 1?

• As a parabolic curve

• As a diagonal line

• As a horizontal line

• As a vertical line

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CCSS.8.EE.B.5

What is the slope of the line G(x) = -x - 2 for x < 1?

• 1

• 0

• -1

• 2

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CCSS.HSF-IF.C.7B

In a three-piece function, what does an open circle at x = 2 indicate?

• The function has a minimum at x = 2

• The function has a maximum at x = 2

• The function is not defined at x = 2

• The function is defined at x = 2

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CCSS.HSF-IF.C.7B

What is the equation of the line for the third piece in the three-piece function example?

• F(x) = x + 2

• F(x) = 2x - 4

• F(x) = 1 - x^2

• F(x) = 3

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CCSS.HSF-IF.C.7B

How do you enter a piecewise function into a graphing calculator?

• Type the function as a single equation

• Use the Y= screen and multiply by intervals

• Enter it as a compound inequality

• Use the graphing calculator's test menu

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CCSS.HSF-IF.C.7B

What is a drawback of using a graphing calculator for piecewise functions?

• It cannot graph more than two pieces

• It does not show open and closed points

• It requires a special software update

• It only works for linear functions

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CCSS.HSF-IF.C.7B