Unit 1: Functions and Their Inverses - Review

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning no two different inputs produce the same output.

Front

What does it mean for two functions to be inverses of each other?

Back

Two functions are inverses if the output of one function becomes the input of the other, and vice versa. This means that if f(x) = y, then f⁻¹(y) = x.

Front

How can you determine if a function is one-to-one using its graph?

Back

A function is one-to-one if any horizontal line drawn on the graph intersects the curve at most once.

Front

What is the relationship between the domain of a function and the range of its inverse?

Back

The domain of a function becomes the range of its inverse.

Front

What is the relationship between the range of a function and the domain of its inverse?

Back

The range of a function becomes the domain of its inverse.

Front

What is the graphical representation of inverse functions?

Back

Inverse functions are reflections of each other over the line y = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, switch the x and y in the equation and solve for y.

Front

What is the significance of the line y = x in relation to functions and their inverses?

Back

The line y = x serves as a mirror line; functions and their inverses are symmetric with respect to this line.

Front

If f(-25) = 7, what is f⁻¹(7)?

Back

f⁻¹(7) = -25.

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input is associated with more than one output.