Understanding Rational Functions

What is a rational function composed of?

• A ratio of two polynomials

• A product of two polynomials

• A single polynomial

• A sum of two polynomials

Which of the following is true about the reciprocal function?

• It is continuous everywhere

• It is defined for all real numbers

• It has a discontinuity at x = 0

• It approaches infinity as x approaches zero

As x becomes very large or very small, what does the reciprocal function approach?

• A vertical asymptote at x = 0

• A horizontal asymptote at y = 0

• Negative infinity

• Infinity

What does the limit notation 'lim' represent in the context of rational functions?

• The average value of a function

• The maximum value of a function

• The minimum value of a function

• The behavior of a function as it approaches a certain value

What is a vertical asymptote?

• A point where the function is undefined

• A line that the graph of the function crosses

• A line that the graph of the function approaches but never touches

• A point where the function is zero

How do you determine the domain of a rational function?

• By finding where the denominator is zero

• By finding where both numerator and denominator are zero

• By finding where the function is continuous

• By finding where the numerator is zero

What is a removable discontinuity?

• A point where the function is undefined and cannot be removed

• A point where the function is zero

• A point where the function is undefined but can be simplified out

• A point where the function is infinite

Which of the following is a characteristic of a hole in a rational function?

• It is a point where the function is zero

• It is a vertical asymptote

• It is a point where the function is infinite

• It is a point where the function is undefined but can be canceled out

What happens at a vertical asymptote in a rational function?

• The function is zero

• The function is continuous

• The function approaches infinity or negative infinity

• The function crosses the x-axis

How many types of discontinuities can a rational function have?

• One

• Four

• Two

• Three