Exploring Adding and Subtracting Rational Expressions

The video tutorial covers rational functions, explaining their form and key features such as intercepts, asymptotes, and holes. It demonstrates how to analyze graphs of rational functions and identify these features. The tutorial also provides a step-by-step guide to finding these features algebraically, including factoring and simplifying functions.

What is a rational function?

• A polynomial function of degree 2

• A function that can only take rational numbers as input

• A function represented by the ratio of two polynomials

• A linear function that passes through the origin

What does a hole in the graph of a rational function represent?

• A discontinuity that can be crossed

• A point where the function is not defined due to a zero in the denominator

• A point where the function reaches its maximum value

• A point where the function intersects the y-axis

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

• Multiply the numerator by the denominator and solve for x

• Divide the numerator by the denominator and solve for x=0

• Set the denominator equal to zero and solve for x

• Set the numerator equal to zero and solve for x

What indicates a vertical asymptote in a rational function?

• When the numerator is zero

• When the function crosses the y-axis

• When the denominator is zero

• When the numerator equals the denominator

How can you identify a hole in the graph of a rational function?

• By setting the numerator to zero

• By identifying the x-intercept of the function

• By finding the highest degree of the polynomial

• By finding the common factor in the numerator and denominator that can be cancelled

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

• By dividing the numerator by the denominator

• By finding the derivative of the function

• By setting the numerator equal to zero

• By setting the denominator equal to zero and solving for x

What is the horizontal asymptote of a rational function when the degree of the numerator is less than the degree of the denominator?

• y = 1

• y = 0

• y = the coefficient of the leading term of the numerator

• There is no horizontal asymptote

If the degrees of the numerator and denominator are equal, how do you find the horizontal asymptote?

• By dividing the leading coefficients of the numerator and denominator

• There is no horizontal asymptote

• By adding the leading coefficients of the numerator and denominator

• It is always y = 1

What happens if the degree of the numerator is greater than the degree of the denominator?

• The function does not have a horizontal asymptote

• The horizontal asymptote is y = 0

• The horizontal asymptote is found by subtracting the degrees

• The horizontal asymptote is y = 1

What is the significance of the leading coefficient in determining the horizontal asymptote?

• It is used when the degrees of the numerator and denominator are equal

• It determines the slope of the asymptote

• It is only used when the degree of the numerator is greater

• It is irrelevant in finding horizontal asymptotes