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 if a relation is a function?

Back

A relation is a function if every input value (x) is associated with exactly one output value (y). This can be checked using the vertical line test on a graph.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

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

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

Front

How can you express the domain of a function using inequalities?

Back

The domain can be expressed using inequalities to show the range of x-values for which the function is defined, e.g., -4 ≤ x ≤ 5.

Front

What is the significance of the graph of a linear function?

Back

The graph of a linear function visually represents the relationship between the input and output values, showing how y changes with respect to x.

Front

How do you find the x-intercept of a linear function?

Back

To find the x-intercept, set y (or f(x)) to 0 and solve for x in the equation of the function.