Exploring Inverse Functions Graphically and Conceptually

What is the primary focus when discussing inverse functions in mathematics?

• Determining the reverse or opposite operation of a function

• Finding the highest value of a function

• Calculating the derivative of a function

• Establishing the limit of a function as it approaches infinity

What does the inverse function do to the output of the original function?

• Squares it

• Multiplies it by -1

• Turns it back into the input

• Reduces it by half

If the function f(x) = x^2, what is its inverse?

• f(x) = x^3

• f(x) = 1/x

• f(x) = 2x

• f(x) = sqrt(x)

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

• f(x) = x^3

• f(x) = sqrt(x/3)

• f(x) = x/3

• f(x) = 3/x

In the context of functions and their inverses, what do the domain and range represent?

• Domain and range both represent inputs

• Domain represents outputs, and range represents inputs

• Domain and range both represent outputs

• Domain represents inputs, and range represents outputs

What happens to the domain and range in the inverse of a function?

• They are both doubled

• They remain unchanged

• They are both halved

• They are swapped

How is the inverse of a function graphically represented?

• By swapping the x and y values of each point

• By doubling the x values of each point

• By halving the y values of each point

• By squaring the x and y values of each point

When graphing the inverse of a function, what line is the graph folded over?

• x = y

• y = x

• x = 0

• y = x^2

What visual effect does graphing the inverse of a function have?

• The graph rotates around the origin

• The graph seems to be folded over the line y=x

• It looks like the graph is compressed vertically

• It appears as if the graph is stretched horizontally

In a non-function relationship graph, what characteristic is observed?

• The graph cannot be folded over the line y=x

• Each output has exactly one input

• Each input has exactly one output

• Some inputs may have more than one output