Graphing Piecewise Functions: Key Concepts and Practice

This video tutorial focuses on graphing piecewise functions through various examples. It begins with a simple piecewise function and progresses to more complex ones involving linear, quadratic, and rational components. The tutorial explains how to graph each segment of the piecewise function, using open and closed circles to indicate included and excluded values. By the end, viewers will understand how to graph different types of piecewise functions step by step.

What is the value of f(x) when x is 0 in the first example?

• 5

• 0

• x

• 1

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CCSS.HSF.IF.A.2

How is the graph of f(x) = x represented when x < 0?

• 45-degree line

• Parabola

• Vertical line

• Horizontal line

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CCSS.HSF-IF.C.7B

In the second example, what is the value of f(x) when x is 2?

• 5

• 2

• x + 3

• 3

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CCSS.HSF.IF.A.2

What type of line represents f(x) = 2 for x < 1 in the second example?

• Parabola

• Diagonal line

• Horizontal line

• Vertical line

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CCSS.HSF-IF.C.7B

In the third example, what is the value of f(x) when x is 1?

• 2

• 1

• x + 1

• 3

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CCSS.HSF.IF.A.2

What shape does the graph of f(x) = -x^2 take for x > 1?

• Upward parabola

• Downward parabola

• Horizontal line

• Vertical line

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CCSS.HSF-IF.C.7A

In the fourth example, what is the y-intercept of the line f(x) = 3x + 4?

• 1

• 0

• 4

• 3

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CCSS.8.EE.B.6

CCSS.8.F.A.3

What is the value of f(x) when x is 0 in the fourth example?

• 3

• 4

• 1

• 2

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CCSS.HSF.IF.A.2

In the fifth example, what is the value of f(x) when x is 3?

• 5

• 2

• 3

• 1

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CCSS.HSF.IF.A.2

What type of function is f(x) = 1/x for x < 0 in the fifth example?

• Rational

• Quadratic

• Linear

• Exponential