Overivew of Rational Functions

The video tutorial covers rational functions, focusing on the reciprocal function and its properties, including domain, range, and asymptotes. It explains how transformations affect these properties and delves into identifying vertical and horizontal asymptotes. The tutorial also explores complex rational functions, slant asymptotes, and the concept of discontinuities, providing methods to find intercepts and simplify expressions.

What is the domain of the reciprocal function y = 1/X?

• All real numbers

• All real numbers except 0

• All positive numbers

• All negative numbers

What is the range of the reciprocal function y = 1/X?

• All negative numbers

• All positive numbers

• All real numbers except 0

• All real numbers

How do vertical and horizontal stretches affect the asymptotes of a reciprocal function?

• They only change the horizontal asymptote

• They only change the vertical asymptote

• They do not change the asymptotes

• They change the asymptotes

Which transformations affect the domain and range of a reciprocal function?

• Shifts along the x and y axes

• Reflections about the x-axis

• Vertical and horizontal stretches

• Reflections about the y-axis

What determines the position of a horizontal asymptote in a rational function?

• The degrees of the numerator and denominator

• The coefficients of the terms

• The constant term

• The leading coefficient

What happens to the horizontal asymptote when the degree of the denominator is greater than the numerator?

• It is at y = 0

• It is at x = 0

• There is no horizontal asymptote

• It is at y = 1

When does a rational function have a slant asymptote?

• When the degree of the numerator is less than the denominator

• When the degree of the numerator is equal to the denominator

• When the degree of the numerator is greater than the denominator

• When the function is simplified

What is a hole in the graph of a rational function?

• A point where the graph crosses the y-axis

• A discontinuity that can be removed by simplification

• A point where the graph crosses the x-axis

• A vertical asymptote

How do you find the x-intercept of a rational function?

• Set x equal to zero

• Set both numerator and denominator equal to zero

• Set the denominator equal to zero

• Set the numerator equal to zero

What is the y-intercept of a rational function?

• The point where the graph crosses the y-axis

• The point where the graph has a vertical asymptote

• The point where the graph crosses the x-axis

• The point where the graph has a hole