Graphing Piecewise-defined Functions

This video tutorial explains how to graph a piecewise defined function, which consists of two parts: x + 2 for x < 1 and -2x + 1 for x >= 1. The instructor demonstrates how to graph each part separately, ensuring the function remains valid by adhering to the conditions for each piece. The video also covers how to evaluate the function at specific points, emphasizing the importance of understanding where each piece applies.

What is a piecewise defined function?

• A function that is not continuous.

• A function defined by multiple equations over different intervals.

• A function that fails the vertical line test.

• A function defined by a single equation.

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CCSS.HSF-IF.C.7B

Why can't we graph both pieces of a piecewise function from left to right?

• It would fail the horizontal line test.

• It would not intersect the y-axis.

• It would not be a function anymore.

• It would be too complex to graph.

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CCSS.HSF-IF.C.7B

What is the y-intercept of the function X + 2?

• (2, 0)

• (0, 2)

• (0, 1)

• (1, 2)

For which values of X is the function X + 2 defined?

• X > 1

• X ≤ 1

• X < 1

• X ≥ 1

What is the slope of the function -1/2 X + 1?

• 1/2

• -1/2

• -1

• 1

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CCSS.8.EE.B.5

At which point does the function -1/2 X + 1 start?

• (1, 1/2)

• (1, 1)

• (0, 1)

• (2, 0)

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CCSS.HSF-IF.C.7A

What happens to the function X + 2 at X = 1?

• It has an open circle.

• It becomes undefined.

• It intersects with -1/2 X + 1.

• It continues as a solid line.

Tags

CCSS.HSF-IF.C.7B

What is the value of the piecewise function at X = 1?

• 0

• 2

• 1/2

• 1

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CCSS.HSF.IF.A.2

Which part of the piecewise function takes the value X = -5?

• Neither part

• Both parts

• -1/2 X + 1

• X + 2

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CCSS.HSF.IF.A.2

What is the value of the piecewise function at X = 4?

• 1

• -2

• 0

• -1

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CCSS.HSF.IF.A.2