Adding and Subtracting Rational Expressions

The video tutorial explains how to determine the domain and range of continuous graphs using inequalities. It introduces the pencil method to identify x and y values that touch the graph. Various examples, including V shape functions, circles, and squares, are used to illustrate the concepts. The tutorial also covers scenarios with open and closed circles and emphasizes the importance of understanding arrow directions in graphs.

What type of mathematical notation is typically used to represent the domain and range of continuous graphs?

• Inequalities

• Whole numbers

• Decimal numbers

• Fractional notations

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

When scanning a graph from left to right to find the domain, what are you trying to identify?

• The lowest point of the graph

• The y-values where the graph is touched

• The highest point of the graph

• The x-values where the graph is touched

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

In a V-shaped graph, if the graph is touched at all x-values, how is the domain expressed?

• All real numbers

• Numbers greater than zero

• Only positive numbers

• Only negative numbers

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

For a circle graph, how would you describe the domain if the graph is only touched between two specific points?

• Only at zero

• All real numbers

• Undefined

• Between two values with inequalities

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

What does it indicate if arrows are present at the ends of a function in a graph?

• The function reverses direction

• The function only exists at that point

• The function stops at that point

• The function continues indefinitely

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

How is the range expressed if a graph continuously touches all y-values?

• All real numbers

• Only negative numbers

• No real numbers

• Only positive numbers

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

What does an open circle on a graph typically signify about the value at that point?

• The value is included in the domain or range

• The value is the lowest point

• The value is the highest point

• The value is not included in the domain or range

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

If a graph has a closed circle at a point, how is this typically represented in inequalities?

• Greater than or equal to the value

• Not equal to the value

• Less than the value

• Equal to the value only

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CCSS.6.EE.B.8

When determining the range by scanning up and down, what are you specifically looking for?

• Y-values where the graph is touched

• X-values where the graph is touched

• The lowest y-value

• The highest y-value

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

How would you describe the domain of a graph that touches the x-axis at only one specific point?

• All real numbers

• X equals the specific point

• Undefined

• No real numbers

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5