Understanding Graphs and Inverse Functions

The video tutorial explains how to use the graph of a function, f(x), to determine specific function values and graph its inverse. It demonstrates finding f(1) graphically and explains the process of plotting the inverse function on the same coordinate plane. The tutorial also covers calculating the derivative of the inverse function, emphasizing the relationship between the slopes of tangent lines on the function and its inverse. Key concepts include graph analysis, inverse functions, and derivative calculations.

What is the value of f(1) based on the graph?

• -3

• 1

• 3

• 5

Which point is used to graph f^(-1)(x) from f(x)?

• (1, -3)

• (3, 1)

• (0, -5)

• (5, 0)

What is the y-intercept of the inverse function f^(-1)(x)?

• (3, 1)

• (1, 3)

• (0, -5)

• (5, 0)

How do the graphs of a function and its inverse relate on a coordinate plane?

• They are parallel.

• They are identical.

• They intersect at the origin.

• They are reflections across the line y = x.

What is the slope of the tangent line to f^(-1)(x) at x = -3?

• 1/2

• 2

• 1

• 3

What is the relationship between the slopes of tangent lines of f(x) and f^(-1)(x)?

• They are negative reciprocals.

• They are unrelated.

• They are reciprocals.

• They are equal.

If f(1) = -3, what is f^(-1)(-3)?

• 1

• -3

• 3

• 0

What is the derivative of f(x) at x = 1 if the slope of f^(-1)(x) at x = -3 is 1/2?

• 2

• 1

• 1/2

• 3

Which of the following points is on the graph of f(x) if (3, 1) is on f^(-1)(x)?

• (1, 3)

• (0, 5)

• (3, 1)

• (1, -3)

What is the formula for the derivative of the inverse function at a point?

• f^(-1)'(x) = -f'(x)

• f'(x) = f^(-1)'(x)

• f'(x) = 1 / f^(-1)'(x)

• f^(-1)'(x) = 1 / f'(x)