Exploring Inverse Linear Functions

What is required for a function to have an inverse?

• It must pass the vertical line test only.

• It must have a slope of 1.

• It must pass both the vertical and horizontal line tests.

• It must be linear.

What does it mean for a function to be one-to-one?

• It can be graphed as a straight line.

• It has no repeating y-values for different x-values.

• It passes the vertical line test only.

• It has a constant slope.

How can you quickly verify if y = 2x - 4 is a one-to-one function?

• By calculating its slope.

• By checking if it passes the horizontal line test only.

• By ensuring it is a linear equation.

• By checking if it passes both the vertical and horizontal line tests.

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

• They are parallel to each other.

• They have the same slope.

• They are reflections across the line y = x.

• They intersect at the origin.

How do you graph the inverse of a function on the same grid?

• By halving the y coordinates.

• By shifting the graph to the right.

• By doubling the x coordinates.

• By flipping the x and y coordinates of each point.

What is the equation of the inverse of y = 2x - 4?

• y = -1/2x + 2

• y = 1/2x - 2

• y = 2x + 4

• y = 1/2x + 2

Which method is commonly used to find the inverse of a function?

• Subtracting terms from both sides

• Switching x and y and solving for y

• Multiplying each term by the slope

• Dividing each term by the y-intercept

What is the slope of the inverse of the function y = 2x - 4?

• 2

• -2

• 1/2

• -1/2

What is the y-intercept of the inverse of the function y = 3x + 9?

• 15

• 9

• 1/3

• 3

Which function does not have an inverse that is also a function?

• y = x

• y = 1/x

• y = x^2

• y = 2