# How do you find the domain and range of # y = -sqrt(x+6)+7 #?

The domain is

The role is

Consequently,

graph{sqrt(x+6)+7 [-28.34, 23.65, 71.9, -32.17]}

By signing up, you agree to our Terms of Service and Privacy Policy

To find the domain of the function ( y = -\sqrt{x + 6} + 7 ), we need to determine the values of ( x ) for which the function is defined. Since we cannot take the square root of a negative number in the real number system, the expression under the square root, ( x + 6 ), must be greater than or equal to 0:

[ x + 6 \geq 0 ]

Solving for ( x ), we have:

[ x \geq -6 ]

So, the domain of the function is ( x \geq -6 ).

To find the range of the function, we need to consider the behavior of the function as ( x ) varies. Since the square root function is always non-negative, ( -\sqrt{x + 6} ) will always be less than or equal to 0. Adding 7 to this result will yield values ranging from 7 down to 7 minus the maximum value of ( -\sqrt{x + 6} ). As ( x ) increases without bound, ( -\sqrt{x + 6} ) decreases without bound. Thus, the range of the function is:

[ y \leq 7 ]

Therefore, the domain of the function is ( x \geq -6 ) and the range is ( y \leq 7 ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the range of the graph of #y = 5(x – 2)^2 + 7#?
- How do you simplify #7p + q - p + 2q/3#?
- How do you evaluate #1\frac { 1} { 2} \times 7#?
- What is the domain and range of {(1,4) (0,-2) (2,3) (-1,4) (-3,0)?
- A student accidentally poured 2 liters of 20% acid solution into a container having 10 liters of 15% acid solution. What is the concentration of the new solution?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7