Question

Choose the best multiple choice option below! Thanks in advance!

Answer 1

• Q5. D,
• Q6. D,
• Q9. B.

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Question 5

The range of the given function has one restriction, its denominator can't be zero, hence:

• 3x + 4 ≠ 0 ⇒ 3x ≠ - 4 ⇒ x ≠ - 4/3

Therefore the function can get any value but zero:

• y ≠ 0

The matching answer choice is D.

Question 6

Linear function is f(x) = mx + b.

Reciprocal of a function f(x) is 1/f(x).

So the reciprocal of linear function has a form of f(x) = 1 / (mx + b).

The only answer choice in same form is D.

Question 9

Substitute x = - 5/3 into function to get:

• 
  `f(x)=\cfrac{1}{3*(-5/3)+5} =\cfrac{1}{-5+5} =\cfrac{1}{0}`

This is undefined value, therefore it represents the vertical asymptote.

The function gets close to - ∞ when x → - 5/3 from left and gets close to +∞ when x → - 5/3 from right (see attached graph).

Therefore the correct choice is B.