Find the domain of f(x)=x+4f\left(x\right)=\sqrt{x+4}f(x)=x+4 . Express your answer using interval notation.

Dom: [ − 4 , ∞ ) \left[-4,\infty\right) [ − 4 , ∞ )

Find the domain of f ( x ) = x + 4 f\left(x\right)=\sqrt{x+4} f ( x ) = x + 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> . Express your answer using interval notation.

Hey, everyone. So let's see if we can solve this problem. In this problem, we are given the function f of x is equal to the square root of x plus 4, and we're asked to find the domain of this function and express our answer using interval notation. Now to find the domain of a function, when it's written as an equation is to think of any values that could possibly break the equation that you have. And in this problem, we have a square root, and you can break a square root. What you want for a square root is you want everything underneath the square root to be positive. So if you ever have a negative number, the square root is going to break. So basically, we could say everything inside the square root to x plus 4 has to be greater than or equal to 0. Now what I can do from here because and by the way the reason I wrote it like this is because I'm basically saying this entire quantity has to be above 0 or equal to 0. It can never be less than 0 because that would be a negative number. Now what I can do from here is solve this like a mini equation by subtracting this 4 on both sides. That'll get the 4s to cancel on the left, giving me that x has to be greater than or equal to negative 4. So what this restriction here is basically saying is x can be any value that is greater than or equal to negative 4. If you're ever less than negative 4, though, that means your function is going to break. So what we could say for our domain is that our x values can go from negative 4, including this value, all the way up to positive infinity. And this right here is the domain for our function. So that is how you can find the domain of the square root of x+4. Hopefully, you found this video helpful, and let's move on.

Find the domain of f ( x ) = x + 4 f\left(x\right)=\sqrt{x+4} f ( x ) = x + 4 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z"> . Express your answer using interval notation.

Dom: [ − 4 , ∞ ) \left[-4,\infty\right) [ − 4 , ∞ )

Dom: [ 4 , ∞ ) \left[4,\infty\right) [ 4 , ∞ )

Dom: [ − 4 , 2 ] \left[-4,2\right] [ − 4 , 2 ]

Dom: [ 2 , 4 ] \left[2,4\right] [ 2 , 4 ]

3. Functions

Intro to Functions & Their Graphs

College Algebra

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Intro to Functions & Their Graphs

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Multiple Choice

Find the domain of $f\left(x\right)=\sqrt{x+4}$ . Express your answer using interval notation.

Dom: $\left[4,\infty\right)$

Dom: $\left[-4,2\right]$

Dom: $\left[2,4\right]$

Dom: $\left[-4,\infty\right)$

Verified step by step guidance

Identify the function given: $ f(x) = \sqrt{x + 4} $. This is a square root function.

Recall that the expression inside the square root must be greater than or equal to zero for the function to be defined. Therefore, set up the inequality: $ x + 4 \geq 0 $.

Solve the inequality $ x + 4 \geq 0 $ by subtracting 4 from both sides to isolate $ x $. This gives $ x \geq -4 $.

The solution to the inequality $ x \geq -4 $ indicates that the domain of the function is all real numbers greater than or equal to -4.

Express the domain in interval notation: $[-4, \infty)$. This means the function is defined for all $ x $ values starting from -4 and extending to positive infinity.

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