Final answer:
The equation of the translated function is f(x) = (x + 1)^2 + 5.
Step-by-step explanation:
The equation of the translated function can be determined by looking at the changes being made to the original function. In this case, the translation is happening in the x-direction by a specific distance. The options given are:
A) f(x) = (x - 1)^2 - 5
B) f(x) = (x + 1)^2 + 5
C) f(x) = (x - 5)^2 - 1
D) f(x) = (x + 5)^2 + 1
To find the correct equation, we need to analyze the changes being made. In option B, the function is being translated in the positive x-direction by a distance of 1 unit, and the y-values are being increased by 5 units. Therefore, the equation of the translated function is f(x) = (x + 1)^2 + 5.