Question

If function f(x)=x is vertically translated 1 unit up and then reflected across the axis. What's the new function in terms of g(x)?

a) g(x)=−x+1

b) g(x)=x−1

c) g(x)=−x−1

d) g(x)=x+1

Answer 1

The new function g(x) after a vertical translation up by 1 unit and a reflection across the x-axis is g(x) = -x - 1.

Step-by-step explanation:

The original function is f(x) = x. When a function is vertically translated one unit up, it becomes f(x) = x + 1. However, when this new function is reflected across the x-axis, every y-value changes sign, hence the function becomes g(x) = - (x + 1) = -x - 1. Therefore, the new function in terms of g(x) after a vertical translation by 1 unit up and reflection across the x-axis is g(x) = -x - 1, which corresponds to option c).