Rational Functions and Discontinuities

The video tutorial covers rational functions, focusing on their domains, continuous and discontinuous functions, and types of discontinuities such as point and removable discontinuities. It explains vertical asymptotes and how to find them by setting the denominator to zero. The tutorial also covers factoring polynomials to identify discontinuities and finding X and Y intercepts. Practice problems are provided to reinforce the concepts discussed.

What is a rational function?

• A ratio of two polynomials.

• A function that cannot be graphed.

• A function with no domain restrictions.

• A function that is always continuous.

Which of the following is NOT part of the domain of a rational function?

• All real numbers.

• Numbers that make the denominator zero.

• Positive integers.

• Negative integers.

What characterizes a continuous function?

• It has undefined points.

• It can be drawn without lifting the pencil.

• It requires lifting the pencil when drawing.

• It has breaks in the graph.

What is a point discontinuity?

• A break in the graph where the function is undefined.

• A continuous part of the graph.

• A point where the graph intersects the x-axis.

• A point where the graph intersects the y-axis.

What is a removable discontinuity?

• A discontinuity that cannot be canceled.

• A discontinuity that can be canceled by factoring.

• A point where the graph is continuous.

• A point where the graph is undefined.

How do you identify a non-removable discontinuity?

• By finding a common factor in the numerator and denominator.

• By checking if the discontinuity can be canceled.

• By ensuring the denominator is never zero.

• By finding a factor that cannot be canceled.

What is the first step in finding the domain of a rational function?

• Factor the numerator.

• Graph the function.

• Set the denominator equal to zero.

• Set the numerator equal to zero.

What is the x-intercept of a rational function?

• Where the numerator equals zero.

• Where the denominator equals zero.

• Where the graph crosses the y-axis.

• Where both numerator and denominator equal zero.

How do you find the vertical asymptote of a rational function?

• By setting the denominator equal to zero.

• By setting the numerator equal to zero.

• By finding the y-intercept.

• By finding the x-intercept.

What is the horizontal asymptote of a rational function?

• A line the graph never approaches.

• A line the graph crosses at the x-intercept.

• A line the graph approaches as x goes to infinity.

• A line the graph crosses at the y-intercept.