Linear Functions Review

Front

What is the DOMAIN of a function?

Back

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 slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

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, represented as (0, b) in the equation y = mx + b.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

What is the significance of the slope in a real-world context?

Back

The slope represents the rate of change, such as speed in a distance-time graph or cost per item in a cost graph.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: y = (-A/B)x + (C/B).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value).

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase, and decreasing if its output values fall as the input values increase.

Front

What is a linear inequality?

Back

A linear inequality is similar to a linear equation but uses inequality signs (>, <, ≥, ≤) instead of an equal sign.