Understanding Oblique Asymptotes and Graphing Rational Functions

What is the condition for a rational function to have an oblique asymptote?

• The degree of the numerator is equal to the degree of the denominator.

• The degree of the numerator is two more than the degree of the denominator.

• The degree of the numerator is one less than the degree of the denominator.

• The degree of the numerator is one more than the degree of the denominator.

What is the equation of an oblique asymptote derived from the division of polynomials?

• y = ax^2 + bx + c

• y = c

• y = mx + b

• y = ax + b

Which division method is preferred when the divisor is linear with a leading coefficient of one?

• Synthetic division

• Long division

• Matrix division

• Polynomial division

Why is the remainder ignored when finding the equation of an oblique asymptote?

• It affects the slope

• It affects the y-intercept

• It does not affect the location of the asymptote

• It is always zero

When graphing rational functions, what is the first step after identifying oblique asymptotes?

• Determine the domain

• Find the y-intercept

• Use a graphing calculator

• Factor the function to see if anything cancels

What is the domain of a rational function with a vertical asymptote at x = 0?

• All real numbers

• All x except x = 0

• All x greater than 0

• All x less than 0

What tool is recommended to ensure accurate placement of hyperbolic curves when graphing?

• A protractor

• A compass

• A ruler

• A graphing calculator

What is the range of a rational function with hyperbolic curves extending infinitely?

• All y less than 0

• All y greater than 0

• All y except y = 0

• All real numbers

In problem-solving, what happens if the degree of the numerator equals the degree of the denominator?

• There is a slant asymptote

• There is a horizontal asymptote

• There is no asymptote

• There is a vertical asymptote

What should be done if the divisor in synthetic division is not linear with a leading coefficient of one?

• Multiply the divisor by a constant

• Use synthetic division anyway

• Use long division

• Ignore the divisor