Explore Linear Functions and Relationships

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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 slope of a linear function represent?

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The slope of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

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What is the y-intercept in a linear function?

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The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by the value of b in the function f(x) = mx + b.

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How do you determine if a relation is a function?

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A relation is a function if each input (x-value) is associated with exactly one output (y-value). This means no x-value can be repeated with different y-values.

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What is the domain of a function?

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

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What is the range of a function?

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

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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How do you find the value of a function at a specific point?

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To find the value of a function at a specific point, substitute the x-value into the function and simplify to find the corresponding y-value.

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What is the difference between a function and a non-function?

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A function has a unique output for each input, while a non-function may have multiple outputs for a single input.

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What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

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The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).