Linear Functions-Flashcard 1

Front

What is a linear function?

Back

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.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the function f(x) = mx + b.

Front

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

Back

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

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.

Front

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.

Front

Write the equation of a line with slope 3 that passes through the point (2, 5).

Back

The equation is y = 3x - 1.

Front

What is the function rule for the linear function that passes through the points (1, 2) and (3, 6)?

Back

The function rule is f(x) = 2x.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.