Reciprocal Functions and Transformations

The video tutorial explains how to find the reciprocal of a linear function, transforming it into a rational function. It covers the restrictions, domain, and range of the reciprocal function, and analyzes intercepts and asymptotes. The tutorial includes graphing the reciprocal function, identifying invariant points, and understanding transformations. Practice problems are provided to reinforce learning.

What happens to a linear function when you find its reciprocal?

• It becomes an exponential function.

• It remains a linear function.

• It becomes a rational function.

• It becomes a polynomial function.

What is the y-intercept of the line y = 0.5x - 2?

• 0

• 2

• 0.5

• -2

Why is the line y = 0.5x - 2 converted to decimal form?

• To find its x-intercept.

• To change its slope.

• To make it easier to graph.

• To simplify the reciprocal calculation.

What is the restriction for the reciprocal function 1/(0.5x - 2)?

• x cannot be -2

• x cannot be 4

• x cannot be 2

• x cannot be 0

What is the domain of the reciprocal function 1/(0.5x - 2)?

• All real numbers except x = -2

• All real numbers except x = 0

• All real numbers

• All real numbers except x = 4

Does the reciprocal function 1/(0.5x - 2) have an x-intercept?

• Yes, at x = 0

• No, it does not have an x-intercept

• Yes, at x = 4

• Yes, at x = 2

What is the horizontal asymptote of the reciprocal function 1/(0.5x - 2)?

• x = 0

• x = 4

• y = 0

• y = 2

What transformation occurs when graphing the reciprocal function 1/(0.5x - 2)?

• Shifted 2 units down

• Shifted 2 units up

• Shifted 4 units to the right

• Shifted 4 units to the left

What is always true for the reciprocal of a linear function y = mx + b?

• It has a y-intercept at y = 0.

• It has a vertical asymptote at x = 0.

• It has a horizontal asymptote at y = 0.

• It has an x-intercept.

What is the y-intercept of the reciprocal function 1/(mx + b)?

• b/m

• 1/b

• 1/m

• m/b