This is what I tell my students with a radical problem like this

right something I tell my students all the time whenever you're having a b in front or any kind of number in front of your ex inside of your function you got to factor that number out see what we're trying to do is we're trying to get our function in this form this is going to be a times square root of B times x minus C plus d so we want our coefficient of x to be one you can see right now our coefficient is two-thirds and so what we need to do then the most common way to be able to factor it out or to rewrite an expression as a product multiplying is to factor how do you factor out a two-thirds I think it's pretty easy when you say like 2 2x plus 4. it's like how do you factor it out when you say oh they have in common of two so you factor out the 2 right X plus two and you're like okay good like I know how to factor and you can always check your work right multiply it back out and you get a 2X plus 4. how the heck do you factor out of two-thirds because I don't know what two-thirds basically goes into there let's go and take a look at a different way that we can do this so I have a two-thirds X Plus One how can I factor out the two thirds well a lot of times when you're thinking about factoring it can be overwhelming because you're like I don't know what they have in common like what is a two-thirds and a one have in common that I can factor out so then it kind of brings it to the point of like well technically when you're factoring out what exactly are you doing we said we're taking out the common factor of two but what exactly does that mean if you look at this basically what I'm doing is I'm taking a 2X dividing it by 2 to give me X I'm taking a 4 divided by 2 and and that's given me a two so I'm taking whatever number I'm dividing both of these terms by I'm putting it on the outside all right so two-thirds whenever I divide that number so when I take that term divided by two whatever is left over I'm going to put inside this parenthesis so let's go and do this 2 3 x divided by two-thirds well that's just going to be an X this one might be a little confusing what is 1 divided by two-thirds but there are some things you do know so let's go and take a look at that if I have one divided by two thirds you recognize they're like oh yeah you can't divide by fractions right you need to get rid of your fraction you multiply by the reciprocal so you multiply by three halves on both sides so therefore that goes to one so you have a three halves divided by one which is just going to be a three-halves so therefore this is X plus a three-halves and if you think about it guys that actually makes sense because when you multiply back out right remember how we multiply this 2 times x is 2x 2 times 2 is 4. when you multiply this back over you have a two-thirds times x which is a two-thirds X you multiply two-thirds times a three-half those are reciprocals of each other that's going to give you back to a one now way to rewrote this I also don't like having my D in front sometimes you'll see that a lot in textbooks or on math problems let's go and put that out there right I like having my D here remember there was no addition or subtraction sign in front of the one but therefore if there's nothing in front of it we can assume that our presume that is going to be a positive because obviously if I had a negative in front of it it would be represented as a negative so now I don't want you to see here is we have a lot of operation we have a reflection on the outside so therefore if it's a vertical reflection that's going to be a reflection about the x-axis we have a vertical shift up one then inside here we have a horizontal let's see if it's less than between 0 and 1 it's going to be a horizontal stretch so we have a horizontal stretch of two-thirds as well as a horizontal shift of three halves what are we going to graph first well the main important thing that I want you to understand is the way I like to do this is I like to break this apart in two parts the first part is going to be the orientation all right what I want to do is I want to know all right where is this graph going so we know that the y equals the square root of x looks like this okay so now What's Happening Here is this graph is being reflected about the x-axis right so now it's so take this graph it's being reflected about the x-axis and then we're having a horizontal stretch of two-thirds so I'm not going to be exact here guys I'm just going to say all right it's going to be horizontal stretch so it's going to be a little bit skinnier or something like that right all right the next one the next step is going to be the translations that is going to be everything left and right so you can see here we're going to be shifting it left three halves and then up one so all I'm simply going to do here so if I'm going to go by ones right we're going left three halves so that's one and one half right so one and one half and then we're going to go up one so it's right there so what I'm doing is I'm basically just taking this coordinate point which is at zero zero I'm shifting it left one and one half going up one and then I'm just gonna like basically copy paste my translation here to go ahead and do this and let's say you know look something like that now we can identify the domain and range because again this is very very important to recognize how far left is this graph well that's going to be at a negative three halves how high is this graph right well that's at a one the reason why that's important is because when I want to identify my domain and range let's actually and let me graph this so so you just make sure you go from there and then you shift it left to right all right so let's go and figure out my domain is domain is going to be basically how far left the graph is going which in this case is going to be a negative three halves how far to the right it's going which is going to be a positive infinity and then the range is going to be basically how low does the graph go which is going to be from negative Infinity to how high is it going to go which is going to be a positive one hopefully this video brought you some value in being able to identify the Transformations and grab it and if so I know the next video is going to give you value as well cheers