Determining Inverse Functions and Their Representations

What does a one-to-one function imply?

• Each input has exactly two outputs.

• Each output is associated with exactly one input.

• The function passes both the vertical and horizontal line tests.

• The function can only be linear.

What is the purpose of the vertical line test?

• To identify the domain of a function.

• To check the linearity of a function.

• To find the inverse of a function.

• To determine if a graph represents a function.

How does the horizontal line test relate to inverse functions?

• It checks if the inverse is also a function.

• It determines the slope of the inverse function.

• It identifies the range of the inverse function.

• It verifies the linearity of the inverse function.

What is the first step in finding the inverse of a function?

• Interchange x and y.

• Solve for y.

• Replace f(x) with y.

• Rewrite the function as f inverse of x.

Why might a function not have an inverse that is also a function?

• If it has a restricted domain.

• If it is not a linear function.

• If it fails the vertical line test.

• If it fails the horizontal line test.

What does the failure of the horizontal line test indicate about a function?

• It does not have an inverse.

• Its inverse is not a function.

• Its inverse is a linear function.

• It is not a one-to-one function.

What transformation is applied to the variables when finding an inverse function?

• Multiplying x and y.

• Dividing x by y.

• Interchanging x and y.

• Adding x to y.

How is the inverse of a linear function found?

• By plotting the graph.

• By interchanging x and y and solving for y.

• By solving for x.

• By applying the horizontal line test.

What is the correct expression for the inverse of a function represented as f(x)?

• x = f(y)

• y = f-1(x)

• f(x) = y

• f-1(x)

What is a key consideration when determining the domain of an inverse function?

• It should include all real numbers.

• It should be identical to the original function's domain.

• It must pass the vertical line test.

• It must not include zero.