Question

Pls help what is the range of y=√x+7+5?

Answer 1

Based on your data, the geometric figure formed by $y= \sqrt{x+7} + 5$ is a parabola. 

The domain for this is x ≥ -7
The range for this is y≥ 5

Answer 2

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,∞)