Exploring Inverse Functions and Their Graphs

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

• They have the same domain and range.

• They have identical equations.

• They have the same graph.

• They cancel each other out when composed.

What is the result of composing a function with its inverse?

• The original input variable

• The original function

• The derivative of the function

• The integral of the function

What is the graphical relationship between a function and its inverse?

• They intersect at the origin.

• They have parallel slopes.

• They are reflections over the y-axis.

• They are reflections over the line y = x.

How can you visually verify if two functions are inverses?

• Their graphs have the same slope.

• Their graphs are reflections over the line y = x.

• Their graphs are identical.

• Their graphs intersect at one point.

What does the vertical line test determine?

• If a graph represents a function.

• If a graph represents an inverse function.

• If a function is quadratic.

• If a function is linear.

What does the horizontal line test determine?

• If a function is quadratic.

• If a function is linear.

• If the inverse of a graph is a function.

• If a graph represents a function.

What does failing the vertical line test indicate?

• The graph represents a linear function.

• The inverse of the graph is a function.

• The graph does not represent a function.

• The graph represents a function.

How do you find the inverse of a function?

• Swap the x and y variables and solve for y.

• Multiply the function by -1.

• Reflect the function over the y-axis.

• Reflect the function over the x-axis.

What is the significance of the domain in finding the inverse of a function?

• It determines the y-intercept of the inverse function.

• It becomes the range of the inverse function.

• It determines the slope of the inverse function.

• It is irrelevant to the inverse function.

Why is the domain restriction important when finding the inverse of a function?

• It determines the accuracy of the inverse function.

• It affects the shape of the inverse function's graph.

• It ensures the inverse function passes the vertical line test.

• It specifies which part of the function to consider for the inverse.