Graphs 6
4 marks · HardConsider the algebraic form of a reciprocal equation.
Write down the general algebraic form of a reciprocal equation.
Explain how you can identify a reciprocal equation just by looking at its algebraic form.
Give an example of a reciprocal equation and state its asymptotes.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) y = a/x or y = a/(x + b) + c
(b) The variable x appears in the denominator, usually as 1/x, giving a term of the form a/x.
(c) Example: y = 6/x; its asymptotes are x = 0 and y = 0
Common mistakes: Confusing reciprocal with quadratic or cubic; Incorrect asymptotes
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · States or writes down correct general form, e.g., y = a/x or equivalent.
B2 (b) · 2 marks · Explains that a reciprocal equation has x in the denominator (1/x term) and gives a clear explanation.
B3 (c) · 1 mark · Gives a valid example and correctly states the vertical and horizontal asymptotes.
Worked solution
(a) The general algebraic form is y = a/x or y = a/(x + b) + c, where a, b, c are constants.
(b) In a reciprocal equation, the variable x appears in the denominator. For example, an equation with a term of 1/x, such as y = 6/x, is a reciprocal equation.
(c) For example, y = 6/x is a reciprocal equation. Its asymptotes are x = 0 (vertical) and y = 0 (horizontal).