Unit 1 review - modeling linear functions

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What is a linear function?

Back

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?

Back

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 of a linear function?

Back

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 the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

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What is the significance of the registration fee in a linear function model for gym membership?

Back

The registration fee represents the y-intercept in the linear function model, indicating the initial cost before any monthly fees are added.

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How do you evaluate a linear function at a specific point?

Back

To evaluate a linear function f(x) = mx + b at a specific point x = a, substitute a into the function: f(a) = ma + b.

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What does it mean for a function to have a constant rate of change?

Back

A function with a constant rate of change means that the slope is consistent, resulting in a straight line when graphed.

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What is the range of a function?

Back

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 end behavior in the context of linear functions?

Back

End behavior describes how the values of a function behave as x approaches positive or negative infinity.

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How do you interpret the slope in a real-world context?

Back

In a real-world context, the slope indicates how one quantity changes in relation to another, such as cost per month in a gym membership.