Reciprocal Function Concepts

The video tutorial covers the reciprocal function f(x) = 1/x, explaining its transformation using a formula involving parameters a, h, and k. It discusses how these parameters affect the graph, including flipping, stretching, compressing, and shifting. The tutorial also covers the asymptotes and domain/range of the function, and provides instructions for graphing and practice problems.

What is the basic form of the reciprocal function?

• f(x) = x - 1

• f(x) = x + 1

• f(x) = 1/x

• f(x) = x^2

What is the first step in transforming a function?

• Find the derivative

• Solve for x

• Understand the given paragraph

• Graph the function

Which of the following represents the transformation formula?

• a(x + h) - k

• a(x^2 - h) + k

• a(1/x - h) + k

• a(x - h) + k

What does the 'a' in the transformation formula affect?

• Flipping, stretching, and compressing

• Only the asymptotes

• Only the horizontal shift

• Only the vertical shift

How does 'h' affect the graph of a function?

• Shifts it up or down

• Shifts it left or right

• Stretches it vertically

• Compresses it horizontally

What is the role of 'k' in the transformation?

• Shifts the graph up or down

• Shifts the graph left or right

• Changes the slope of the graph

• Flips the graph over the x-axis

Where are the asymptotes located for the reciprocal function?

• x = -1 and y = -1

• x = 1 and y = 1

• x = 0 and y = 0

• x = 2 and y = 2

What is the domain of the reciprocal function?

• All negative numbers

• All positive numbers

• All real numbers except x = 0

• All real numbers

What is the range of the reciprocal function?

• All positive numbers

• All negative numbers

• All real numbers

• All real numbers except y = 0

What is the purpose of understanding transformations?

• To find derivatives

• To graph functions accurately

• To solve equations

• To calculate integrals