2.5 Assignment: Key Characteristics of Linear Functions

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What is a linear function?

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A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What does the domain of a function represent?

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The domain of a function represents all the possible input values (x-values) for which the function is defined.

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What is the range of a function?

Back

The range of a function represents all the possible output values (y-values) that the function can produce.

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How do you find the x-intercept of a function?

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The x-intercept of a function is found by setting y = 0 and solving for x.

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What is the slope of a linear function?

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The slope of a linear function (m) represents the rate of change of y with respect to x. It indicates how steep the line is.

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What is the y-intercept of a linear function?

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The y-intercept (b) is the point where the graph of the function crosses the y-axis, represented as (0, b).

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What does it mean for a function to be defined for all real numbers?

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A function defined for all real numbers means that there are no restrictions on the input values (x-values); it can take any real number.

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What is the significance of the graph of a function?

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The graph of a function visually represents the relationship between the input (x) and output (y) values, making it easier to analyze the function's behavior.

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How can you determine if a relation is a function?

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A relation is a function if each input value (x) corresponds to exactly one output value (y). This can be checked using the vertical line test.

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What is the vertical line test?

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The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.