Understanding Domain of a Function from Graphs

This video tutorial explains how to determine the domain of a function using its graph. It covers several examples, including graphs with closed and open endpoints, mixed endpoints, and infinite domains. The tutorial demonstrates how to express domains using interval notation and inequalities, emphasizing the importance of analyzing graphs from left to right. The video also briefly touches on the concept of range, although the focus remains on domain determination.

What is the domain of a function?

• The set of all possible inputs of a function.

• The set of all possible outputs of a function.

• The graph of a function.

• The range of a function.

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In interval notation, how is a closed endpoint represented?

• With a bracket.

• With a comma.

• With a dash.

• With a parenthesis.

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For a graph with a closed endpoint at -1 and extending to infinity, what is the domain?

• (-∞, 1]

• [-∞, 1)

• [-1, ∞)

• (-1, ∞)

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How is an open endpoint at -4 represented in interval notation?

• (-∞, 4]

• (-4, ∞)

• [-∞, 4)

• [-4, ∞)

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What is the interval notation for a domain that does not include its starting point?

• Use a parenthesis at the start.

• Use a bracket at the start.

• Use a dash at the start.

• Use a comma at the start.

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If a graph starts at an open point -3 and ends at a closed point 6, what is the domain?

• (-3, 6)

• [-3, 6]

• [-3, 6)

• (-3, 6]

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Which of the following is true for a closed endpoint?

• It is not included in the domain.

• It is always at zero.

• It is always at infinity.

• It is included in the domain.

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What does it mean if a graph extends infinitely in both directions?

• The domain includes all real numbers.

• The domain is undefined.

• The domain is limited to negative numbers.

• The domain is limited to positive numbers.

How is the domain of a function expressed if it includes all real numbers?

• (-∞, ∞)

• [0, ∞)

• (-∞, 0]

• [0, 0]

What is the inequality representation for a domain that includes all real numbers?

• x < 0

• x is a positive integer

• x > 0

• x is any real number