Reciprocal Function Concepts

The video tutorial introduces the reciprocal function, f(x) = 1/x, highlighting its unique features and behavior near x = 0, where the function is undefined. The instructor uses tables of values to explore the function's behavior for positive and negative x values, plotting these on a graph to illustrate the general shape. The graph is analyzed for its asymptotic behavior, with vertical and horizontal asymptotes identified. Finally, the domain and range of the function are determined, noting that x and y cannot be zero.

What is the reciprocal function also known as?

• Exponential function

• Reciprocal function

• Quadratic function

• Inverse function

Why can't the x-value be zero in the reciprocal function?

• It results in a positive value

• It results in a zero value

• It results in a negative value

• It results in an undefined value

What happens to the y-value as x approaches zero from the positive side?

• Y approaches infinity

• Y approaches zero

• Y remains constant

• Y approaches negative infinity

What is the y-value when x is 0.1 in the reciprocal function?

• 0.1

• 100

• 1

• 10

What happens to the y-value as x approaches zero from the negative side?

• Y approaches zero

• Y remains constant

• Y approaches infinity

• Y approaches negative infinity

What is the y-value when x is -0.1 in the reciprocal function?

• -10

• -0.1

• -1

• -100

What is the general shape of the graph of the reciprocal function?

• Linear

• Circular

• Hyperbolic

• Parabolic

What is an asymptote in the context of the reciprocal function?

• A vertex of the graph

• A point the graph passes through

• A line the graph never touches

• A curve the graph follows

Where is the vertical asymptote located in the reciprocal function?

• X = 1

• X = 0

• Y = 1

• Y = 0

Where is the horizontal asymptote located in the reciprocal function?

• Y = 1

• Y = 0

• X = 1

• X = 0