Understanding Inverse Functions

What is the main characteristic of an inverse relation?

• It squares the input values.

• It adds a constant to the input values.

• It interchanges the input and output values.

• It doubles the input values.

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

• It is the axis of symmetry for inverse functions.

• It is the line where all functions intersect.

• It is the line where all inverse functions are parallel.

• It is the line where all inverse functions are perpendicular.

How do you find the inverse of a function?

• By multiplying all terms by 2.

• By switching the x and y values and solving for y.

• By dividing all terms by 3.

• By adding 5 to all terms.

What happens when you take the cube root of a number?

• You must multiply by 3.

• You do not need to consider plus or minus.

• You need to consider plus or minus.

• You must add a constant.

What is the vertical line test used for?

• To determine if a graph is a function.

• To calculate the area under a curve.

• To determine the maximum value of a function.

• To find the slope of a line.

What does the horizontal line test determine?

• If a function is increasing.

• If a function is decreasing.

• If the inverse of a function is also a function.

• If a function has a maximum point.

What is the result of applying the horizontal line test to a function that intersects more than once?

• The inverse is a function.

• The function is linear.

• The inverse is not a function.

• The function is quadratic.

What does it mean if a function passes the horizontal line test?

• The function is not differentiable.

• The inverse of the function is a function.

• The inverse of the function is not a function.

• The function is not continuous.

How can you verify if two functions are inverses of each other?

• By checking if their graphs are parallel.

• By ensuring their product is zero.

• By confirming that f(g(x)) and g(f(x)) both equal x.

• By checking if their sum is a constant.

In the context of inverse functions, what does the term 'domain' refer to?

• The set of all possible output values.

• The set of all possible input values.

• The set of all possible slope values.

• The set of all possible intercept values.