Unit 1: Functions and Their Inverses - Review

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y variables and solve for y.

Front

What is the inverse of the function f(x) = 2x + 3?

Back

f^{-1}(x) = \frac{x - 3}{2}.

Front

If f^{-1}(a) = b, what is f(b)?

Back

f(b) = a.

Front

What is the graphical representation of a function and its inverse?

Back

The graph of a function and its inverse are symmetric with respect to the line y = x.

Front

What is the inverse of the function f(x) = x^2 (for x >= 0)?

Back

f^{-1}(x) = \sqrt{x}.

Front

How do you determine if a function has an inverse?

Back

A function has an inverse if it is one-to-one, meaning it passes the horizontal line test.

Front

What is the horizontal line test?

Back

The horizontal line test states that if any horizontal line intersects the graph of a function more than once, the function does not have an inverse.