Move the slider on the graph on the right to graph each function:

For the function: y=√x-7+1

The domain is : x ≥
The range is: y ≥

The domain the function is

In interval notation: [7,  ∞)

The range of the function is in the interval  (1, ∞).

Given function:

Find the domain of the function:

In this case you do not want a negative argument for the square root (you cannot find the solution of a negative square root, at least as a real number).

What you do it is to "impose" that the argument is always positive or zero (you know the square root of a positive number or zero).

So you set the argument bigger or equal to zero and solve for x to find the ALLOWED values of your variable:

Therefore, the domain the function is

Find the range of the function:

Range of the function is the set of all values of y when we substitute the values of x.

For, x = 7

So, the value of y in the interval (1, ∞).

Therefore, the range of the function is in the interval  (1, ∞).

For more information:

link

The domain is

The range is

Step-by-step explanation:

we have

Find the domain

Remember that

The domain of a function is the set of all possible values of x

we know that the radicand of the function must be greater than or equal to zero

so

solve for x

therefore

The domain is

Find the range

Remember that

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

For x=7

The value of y is equal to

so

The solution for y is the interval [1,∞)

therefore

The range is

f

step-by-step explanation:

f