M2M4: Inverse + Piecewise

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes x to y, then the inverse function f^(-1)(y) takes y back to x.

Front

What is the domain of a function?

Back

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

Front

How do you write the equation of a line in point-slope form?

Back

The point-slope form of a line is given by f(x) = m(x - x_1) + y_1, where m is the slope and (x_1, y_1) is a point on the line.

Front

What is piecewise function?

Back

A piecewise function is defined by different expressions based on the input value. It has different rules for different intervals of the domain.

Front

What does it mean for two functions to be inverses?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain of f and g.

Front

How do you determine if two functions are inverses?

Back

To determine if two functions are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in their respective domains.

Front

What is the modified point-slope form of a line?

Back

The modified point-slope form is f(x) = m(x - x_1) + y_1, where m is the slope and (x_1, y_1) is a specific point on the line.

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).

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line. For example, (a, b) represents all numbers between a and b, not including a and b.