Question

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

Answer 1

Answer:

The new function is $y=\frac{1}{x-5}+3$ , where x ≠ 5

Step-by-step explanation:

The reciprocal parent function is $f(x)=\frac{1}{x}$ , 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  $y=\frac{1}{x}$

∵ 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

∴ $y=\frac{1}{x-5}+3$

The new function is  $y=\frac{1}{x-5}+3$ , where x ≠ 5