One-to-One & Inverse Functions Practice

Front

What is a function?

Back

A relation where each input has exactly one output.

Front

What is a one-to-one function?

Back

A function where each output is associated with exactly one input.

Front

What is the vertical line test?

Back

A method to determine if a relation is a function by checking if a vertical line intersects the graph at more than one point.

Front

What is the horizontal line test?

Back

A method to determine if a function is one-to-one by checking if a horizontal line intersects the graph at more than one point.

Front

What is the inverse of a function?

Back

A function that reverses the effect of the original function, swapping the input and output.

Front

How do you find the inverse of a function algebraically?

Back

Replace f(x) with y, swap x and y, and solve for y.

Front

What does it mean for a function to be not a function?

Back

A relation that does not meet the definition of a function, such as having multiple outputs for a single input.

Front

What is the significance of the line y = x in relation to inverse functions?

Back

The graph of a function and its inverse are reflections over the line y = x.

Front

Give an example of a one-to-one function.

Back

f(x) = 2x + 3 is one-to-one because each output corresponds to one input.

Front

Give an example of a function that is not one-to-one.

Back

f(x) = x^2 is not one-to-one because both f(2) and f(-2) yield the same output.