Question

The reciprocal parent function is translated 5 units right and 3 units up. Write an equation to represent the new function.

Transformations:
y=ax-h+k

Answer 1

The new function is
`y=(1)/(x-5)+3` , where x ≠ 5

Explanation:

The reciprocal parent function is
`f(x)=(1)/(x)` , where x ≠ 0

The translation of f(x) to the right h units is f(x - h)

The translation of f(x) up k units is f(x) + k

The translation of f(x) to the right h units and up k units is f(x - h) + k

∵ The equation of the reciprocal parent function is
`y=(1)/(x)`

∵ The function is translated 5 units right

∴ h = 5

- That means 5 is subtracted from x ⇒ (x - 5)

∵ The function is translated 3 units up

∴ k = 3

- That means y added by 3

∴
`y=(1)/(x-5)+3`

The new function is
`y=(1)/(x-5)+3` , where x ≠ 5