Question

Question #58f14

Answer 1

`"D:"` `{x inRR | x!=0}`
`"R":` `{y inRR | y!=-4}`

Explanation:

Domain and range are a set of values that the function can possibly have. It does not have to be at the same time.

Domain corresponds to the possible `x` values while range corresponds to the possible `y` values.

Because this function is a reciprocal, there are going to be two asymptotes. Normally, these asymptotes are the axes, but since the function was translated to the left 4 units, there will be a new asymptote.

The domain of the base function is `{x inRR | x!=0}`. The range of the base function is `{y inRR | y!=0}`.

With a single transformation applied (translated to the left 4 units), only the range is affected. The new range is `{y inRR | y!=-4}`.

If we graph the function, we can get a visual representation of the function.

graph{y=1/(x+4) [-8.89, 8.89, -4.45, 4.44]}

As you can see, the only value that the function cannot have is `(0, -4)`.

Hope this helps :)