Domain and Range of Functions

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

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

To determine the domain, identify any restrictions on the input values, such as values that would make the denominator zero or result in taking the square root of a negative number.

Interval notation is a way of writing subsets of the real number line, using parentheses and brackets to indicate whether endpoints are included or excluded.

A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.

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).

The y-intercept is found by setting x = 0 in the equation and solving for y.

The slope-intercept form, y = mx + b, allows you to easily identify the slope (m) and the y-intercept (b) of the line.

Gaussian elimination is a method for solving systems of linear equations by transforming the system into an equivalent upper triangular form.

A unique solution means there is one set of values that satisfies all equations; no solution means the equations contradict each other; infinitely many solutions mean there are multiple sets of values that satisfy the equations.