# How do you find the domain and range of #y=sqrt(2x+7)#?

The main driving force here is we can't take the square root of a negative number in the real number system.

So, we need to find the smallest number that we can take the square root of that is still in the real number system, which of course is zero.

So, that is the smallest, legal x value, which is the lower limit of your domain. There is no maximum x value, so the upper limit of your domain is positive infinity.

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To find the domain of the function y = √(2x + 7), you need to identify the values of x for which the function is defined. Since the square root function (√) requires the expression inside it to be non-negative, the expression 2x + 7 must be greater than or equal to zero. Solving 2x + 7 ≥ 0 for x, you get x ≥ -7/2. Therefore, the domain of the function is all real numbers greater than or equal to -7/2, or in interval notation, (-7/2, ∞).

To find the range of the function, consider the behavior of the square root function. The square root of any non-negative number is always non-negative. Therefore, the range of y = √(2x + 7) consists of all non-negative real numbers. In interval notation, the range is [0, ∞).

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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.

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