Question

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

For the function: y = StartRoot x minus 7 EndRoot + 1

The domain is : x ≥

The range is: y ≥

Answer 1

The domain the function is $x\geq 7$.

In interval notation: [7,  ∞).

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

The given function is $y=\sqrt{x-7}+1$.

The domain is x ≥ and the range is y ≥.

What is a function?

A technical definition of a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Now, $x-7\geq 0$

⇒$x\geq 7$

Therefore, the domain the function is $x\geq 7$

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

Now, for $x=7$

$y=\sqrt{7-7}+1=1$

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

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

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