Graphing Inverse Functions Concepts

The video tutorial explains how to graph inverse functions by recalling that if f(x) = y, then f inverse(y) = x. It demonstrates graphing a linear function, f(x) = 2x + 1, and its inverse by plotting points. The tutorial also covers graphing a more complex function, g(x) = sqrt(x + 1) - 2, and its inverse. The video concludes with a discussion on ensuring the graph's ends match and the application of these skills to non one-to-one functions.

What is the relationship between a function and its inverse?

• They are identical.

• They swap inputs and outputs.

• They have the same inputs and outputs.

• They have no relationship.

If f(x) = 2x + 1, what is the output when x = 0?

• 2

• 1

• 0

• 3

Which point is on the graph of the inverse of f(x) = 2x + 1?

• (0, 1)

• (-1, -1)

• (3, 1)

• (1, 3)

How do you graph the inverse of a function without finding it algebraically?

• By using a calculator

• By swapping the x and y coordinates of the points

• By guessing the points

• By drawing a random line

What is the output of f(x) = 2x + 1 when x = 1?

• 4

• 1

• 3

• 2

What is the inverse of the point (1, 0) on the graph of f(x)?

• (1, 1)

• (0, -1)

• (1, 0)

• (0, 1)

What transformation is applied to the function g(x) = √(x + 1) - 2?

• Shift left by 1 and down by 2

• Shift right by 1 and down by 2

• Shift right by 1 and up by 2

• Shift left by 1 and up by 2

Which point is on the graph of the inverse of g(x) = √(x + 1) - 2?

• (3, 0)

• (2, 0)

• (0, -1)

• (-1, -2)

What is the output of g(x) = √(x + 1) - 2 when x = 0?

• -1

• 0

• 1

• -2

What shape does the graph of the inverse of g(x) create?

• A circle

• Half of a parabola

• A straight line

• A full parabola