Question

The graph of F()= is shown below. If you horizontally shift this function left 5 units, what is the equation of the new function?

Answer 1

We have to find the equation of F(x) when it is shifted 5 units to the left.

When translating a function in the horizontal axis, the change in the function happens in the argument of the function.

In this case, we can select a known point of F(x) = 1/x.

We can pick x = 0, where we know that F(x) has its only discontinuity.

Then, for G(x), the translated function, this discontinuity has to be translated 5 units to the left. This means that the discontinity happens at x = -5.

Then, we can write G(x) as:

`G(x)=F(x+5)=(1)/(x+5)`

Answer: G(x) = 1/(x+5) [Option D]