State the domain of the rational function. f(x) = seven divided by quantity fourteen minus x.

Given the three zeros

The other zero will be the conjugate pair of  

Writing these zeros in factorized form of f(x) gives:

→ Multipy out the first two brackets to get

→ Multiply out further

C

Question 2

Given  

Collecting two terms together to get

Notice that each group has common factor  

Factorise the common factor gives

The zeros are  

and four of  

The zero  will give an imaginary results

So, f(x) has one real root and four imaginary root

B

Question 3

The zeros are

and  

and  

which gives two answers:  and  

So the factorized form is  

C

Question 4

If  is one of the zeros of  then the other zero would be to conjugate pair of  which is  

B

Question 5

The denominator must not equal zero because we can't divide a quantity by zero (undefined result)

So, we need to find the value of  that would make the denominator equal to zero

A

Question 6

To find vertical asymptote, set the denominator to zero then find 'x'

and  

A

Question 7

The degree of the denominator is higher than the numerator's, hence the horizontal asymptote is y = 0

Question 8

The degree of numerator is higher than the degree of the denominator, hence no horizontal asymptote

Question 9

To have a horizontal asymptote, , both numerator and denominator must be on the same polynomial degree, and the leading degree have coefficient of 2 and 9

Example:  

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