Reciprocal Functions and Their Properties

The video tutorial explores reciprocal functions, starting with basic concepts of fractions and their reciprocals. It emphasizes visualizing these functions on graphs, identifying key points, and understanding asymptotes. The tutorial guides viewers through graphing reciprocal functions, leading to the exploration of hyperbolas. The focus is on visual learning and understanding the properties of these mathematical concepts.

What is the reciprocal of the fraction 3/5?

• 1/3

• 3/5

• 1/5

• 5/3

When graphing the reciprocal of a function, what happens at points where the original function equals zero?

• The reciprocal is zero

• The reciprocal is negative

• The reciprocal is undefined

• The reciprocal is one

What is the equation of the vertical asymptote for the function y = 1/(x-2)?

• x = -2

• x = 2

• x = 1

• x = 0

As the denominator of a fraction increases, what happens to the value of the fraction?

• It becomes negative

• It increases

• It decreases

• It remains the same

What is the smallest value a reciprocal can approach but never reach?

• One

• Zero

• Infinity

• Negative one

What is the reciprocal of -1?

• -1

• 1

• Undefined

• 0

What shape does the graph of a reciprocal function typically form?

• Circle

• Parabola

• Ellipse

• Hyperbola

If a function has a y-value of 0.5, what is the y-value of its reciprocal?

• 1

• 2

• Undefined

• 0.5

What is the reciprocal of a function at a point where its y-value is 2?

• 0.5

• Undefined

• 2

• 1

What is the reciprocal of a function at a point where its y-value is -0.5?

• -2

• 0.5

• 2

• -0.5