Intercepts, Zeroes and Asymptote of Rational Functions

Which of the following is the set of all values that the variable x can take?

• Range

• Intercept

• Domain

• Zeroes

What is the domain of f(x) = 𝑥−3 / 𝑥+3 ?

• All real numbers

• All real numbers except – 3

• All real numbers except 3

• Cannot be determined

What value/s of x that will make the function meaningless f(x) = 𝑥−1/ 𝑥 ?

• x = -1

• x = 0

• x = 1

• All real numbers

Complete the sentence: The real numbers zeroes are also ____________ of the graph of the function.

• Asymptote

• x – intercepts

• y – intercepts

• Range

Which of the following is the set of all values that f(x) can take?

• Range

• Intercept

• Domain

• Zeroes

What is the range of f(x) =1/ 𝑥

?

• R ={𝑦|𝑦 = 1}

• R ={𝑦|𝑦 = 0}

• R = {𝑦|𝑦 ≠ 1}

• R = {𝑦|𝑦 ≠ 0}

Which of the following is a true statement?

• A rational function is a quotient of functions.

• Asymptotes are a common characteristic of rational functions.

• An asymptote is a line that a graph approaches, but does not touch.

• All of the above.

If the degree of the leading coefficient of the numerator is equal to the degree of the leading coefficient of the denominator of a rational function, which of the following statements has to be true?

• The graph has no asymptote

• The graph of the function has slant asymptote

• The graph of the function has a horizontal asymptote

• None of the above

What is the horizontal asymptote of 𝑓(𝑥) = 𝑥+5 / 3𝑥²

?

• y = 3

• y = 0

• y = - 2

• y = - 3

What is the vertical asymptote of 𝑓(𝑥) = 3𝑥+1/ 𝑥−5

?

• x = 5

• x = 3

• x = 1

• x = 0