Answer:
All positive numbers starting from 5, in other words, y ≥ 5 or Range= [5,∞)
Step-by-step explanation:
First, you have to find the dominion of the function, this is all the numbers x can get to be a real function.
In this case (y=√x+7 +5), the result from adding x+7 has to be 0 or a positive number, because we can´t have negative numbers inside a square root to have a real function.
So x+7≥0; This is our function to find the dominion. We subtract a 7 from both sides of the function: x+7-(7) ≥ 0-(7), or if it is easier we send the 7 to the other side of the function. Doing the operations we get:
Dominion, x ≥ -7, so x can get all the numbers except the numbers that are smaller than -7.
Now we need to know the range of the function, and knowing that we can´t have x smaller than -7 we are going to substitute this -7 in the original function:
y=√-7+7 +5
Now we solve the equation:
y=√0 +5
y=5
so we know that when x=-7, y=5, and if we keep substituting the numbers that x can take (Dominion), then y will be a different number bigger than 5.
Example:
We are going to substitute x with -6 (a bigger number than -7)
y=√-6+7 +5
y=√1 +5
y=1+5
y=6
So we can conclude that our range will be all positive numbers starting at 5.
Range= [5,∞)
