Exploring Inverse Functions and Their Properties

What is the output of a function commonly referred to as?

• Independent variable

• Domain

• Range

• Dependent variable

What operation reverses multiplying by 2?

• Multiplying by 0.5

• Adding 2

• Subtracting 2

• Dividing by 2

How do you find the inverse of a linear equation?

• Subtract the slope from both sides

• Add 1 to both sides

• Multiply both sides by -1

• Swap the x and y variables

What is the graphical representation of an inverse function?

• A reflection over the line y = x

• A perpendicular line

• A parallel line

• A reflection over the y-axis

What does the horizontal line test determine?

• If a graph is a function

• If the inverse of a graph is a function

• The slope of a function

• The y-intercept of a function

What is the inverse function notation for f(x)?

• 1/f(x)

• f(x)-1

• -f(x)

• f-1(x)

What is required to solve for the inverse of a complex function?

• Adding 1 to both sides of the equation

• Factoring out the variable y

• Dividing both sides by 2

• Multiplying both sides by the coefficient of x

How do you verify two functions are inverses of each other?

• They have the same domain and range

• Their graphs are identical

• Composing them returns the original input

• They have opposite slopes

What is the result of restricting the domain of a function?

• It changes the function's slope

• It alters the function's range only

• It eliminates the function's y-intercept

• It ensures the inverse is also a function

What happens to the domain and range when finding an inverse?

• They become undefined

• They swap places

• They remain unchanged

• They both become the range