A.3C Linear functions

Front

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.

Front

What does the domain of a function represent?

Back

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

Front

What does the range of a function represent?

Back

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

Front

How do you determine the domain of a linear function from its graph?

Back

The domain can be determined by identifying the x-values that the graph covers. For example, if the graph extends from x = -4 to x = 5, the domain is -4 ≤ x ≤ 5.

Front

How do you determine the range of a linear function from its graph?

Back

The range can be determined by identifying the y-values that the graph covers. For example, if the graph extends from g(x) = -7 to g(x) = 6, the range is -7 ≤ g(x) ≤ 6.

Front

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). It is represented by the letter m in the function's equation.

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. It is represented by the letter b in the function's equation.

Front

What is the difference between open and closed intervals in domain and range?

Back

An open interval (e.g., -4 < x < 5) does not include its endpoints, while a closed interval (e.g., -4 ≤ x ≤ 5) includes its endpoints.

Front

How can you represent a linear function graphically?

Back

A linear function can be represented graphically by plotting points that satisfy the function's equation and connecting them to form a straight line.

Front

What is the significance of the inequality symbols in domain and range?

Back

Inequality symbols indicate whether the endpoints are included (≤, ≥) or excluded (<, >) in the domain and range.