Question

What is the domain of the function y = Vx+6 - 7?

Answer 1

Answer: Choice B)
`x \ge -6`

If you were to plug x = -6 into the equation, you'd find the x+6 portion turns to 0. Any smaller x value is not allowed because x+6 would be negative. We cannot take the square root of a negative value to get some real number.

Put another way, solving
`x+6 \ge 0` leads to
`x \ge -6`

In terms of transformations,
`y = √(x)` becoming
`y = √(x+6)` means the graph has been shifted 6 units to the left. The original domain
`x \ge 0` becomes
`x \ge -6`, as the domain has also shifted the same 6 units.

Visually, the left most point on the graph will directly determine the smallest domain value. The domain is the set of all allowed x inputs.

The -7 at the end does not affect the domain at all. We can replace it with anything you want, and the domain will still be the same. This value affects the range only.