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What is a linear function?

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A linear function is a function that can be graphically represented in the Cartesian plane 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 y-value changes for a one-unit increase in the x-value.

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What is the y-intercept of 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 the value of the function when x = 0.

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

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A function is increasing if its slope is positive (the line rises as you move from left to right) and decreasing if its slope is negative (the line falls as you move from left to right).

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What is the initial value of a function?

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The initial value of a function is the value of the function at the starting point, often represented by the y-intercept in linear functions.

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How can you identify the greater y-intercept between two functions?

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You can identify the greater y-intercept by comparing the values of the y-intercepts of both functions. The function with the higher y-value at x=0 has the greater y-intercept.

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What does it mean for a function to have multiple increasing intervals?

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Multiple increasing intervals mean that there are several segments on the graph where the function's value increases as x increases.

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

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To find the value of a function at a specific point using a table of values, locate the row corresponding to that x-value and read the corresponding y-value.

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What is the significance of comparing linear functions?

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Comparing linear functions helps to understand their differences in terms of slope, y-intercept, and overall behavior, which is essential for solving real-world problems.

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What is a qualitative graph?

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A qualitative graph provides a visual representation of a function's behavior without specific numerical values, focusing on the general shape and trends.