AR Unit 7 Inverses from Tables and Graphs

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, meaning if f(x) = y, then f^(-1)(y) = x.

Front

What does the notation y^-1(x) represent?

Back

It represents the inverse function of y at the value x.

Front

How do you determine if two functions are inverses of each other?

Back

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

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

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

If h(x) = 2x + 3, what is h^-1(x)?

Back

h^-1(x) = (x - 3)/2.

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function's graph across the line y = x.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

How can you tell if the inverse of a function is also a function?

Back

Use the Horizontal Line Test: if any horizontal line intersects the graph of the function more than once, its inverse is not a function.

Front

What is the significance of the point (a, b) in relation to inverse functions?

Back

If (a, b) is a point on the graph of a function, then (b, a) is a point on the graph of its inverse.