Applying Linear Functions & Analyzing Functions & Graphs

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What is a linear function?

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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 dependent variable (y) changes for a unit change in the independent variable (x).

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What is the y-intercept in a linear function?

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How do you determine if a function is increasing or decreasing?

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A function is increasing if the slope is positive (rises as x increases) and decreasing if the slope is negative (falls as x increases).

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What does it mean for a function to be non-linear?

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A non-linear function does not form a straight line when graphed. Its rate of change varies, and it can have curves, bends, or other shapes.

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How can you tell if a graph represents a linear function?

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This equation represents a linear function where the slope is 35 (indicating a steep increase) and the y-intercept is 10 (indicating the starting value when x=0).

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How do you compare two linear functions?

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To compare two linear functions, look at their slopes and y-intercepts. The function with the higher slope increases faster, while the y-intercept indicates the starting value.

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What does it mean if two functions intersect on a graph?

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If two functions intersect on a graph, it means they have the same value (y) at that point for the same input (x). This is where the two functions are equal.

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What is a function's domain?

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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.