Answer:
The new function is [tex]y=\frac{1}{x-5}+3[/tex] , where x ≠ 5
Step-by-step explanation:
The reciprocal parent function is [tex]f(x)=\frac{1}{x}[/tex] , 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 [tex]y=\frac{1}{x}[/tex]
∵ 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
∴ [tex]y=\frac{1}{x-5}+3[/tex]
The new function is [tex]y=\frac{1}{x-5}+3[/tex] , where x ≠ 5
