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Good day students welcome to mathgotserved.com in this group were going to be going over how to graph exponential functions all right this structure is for the example where going to be graph is as follows we are to graph the given exponential function after that we are to state the domain the domain the range intercepts and asymptotes then are we are to label the graph okay the legal the graph completely so what were going to be doing a is going to be used in the results we got from both the from the property is basically the domain and range intercepts an asymptotes to labeled graph that we generated initially okay right let's go ahead and laugh starts the function on the consideration is why equals two to the X okay so why this and exponential function in the next financial function because the have a number raised to a variable exponent okay so you have any real number race two and a variable exponents and that even X initial term so we have why equals that term so we have an exponential function okay so the graph this one we're going to be making use of the table of values were going to going from negative to all the way to positive two okay so you can use more values of you want the more input and output values you have the more accurate your result is going to be alright so in the middle we have why equals two to the X square will be carry out our computations to determing the output value for each X inputs okay's and out our computations would use please our final output Valley here in the why, so let's start with -2 so this is the inputs what is why going to be why is going to be to raised to the negative to power because in this exponential function the inputs is the X right so we have X of the inputs with simply replace the X in this function with negative to and there were going to simplify okay now the recall the negative power property of exponents also love the reciprocal property of exponents let's go over that real quick so I like is recall that if you have X race to the negative am the negativity of the exponents cause the term with the negative exponents to gets reciprocated right so we have exited negative M to the comes one over X to the am plus an of the reciprocate the term with the negative exponent the power becomes positive alright so let's apply that idea here what is to to the negative to going to be to do negative to become one over to square right and then to squares 2×2 which is one over for so our outputs for this input is one for alright let's move on to the next input value which is negative one so what is our outputs when X is negative one for the same procedure three did in the previous row we just simply negative one for our X will now apply the reciprocal property of exponents so we reciprocate this term here to yield one over to the first power which is just one over to so our outputs when X is negative one is positive one half now to think a look at the zero what the outputs you have to race to the zero power if you raise to to the zero power your your outputs is simply going to be one okay so have one now let's switch to the negative to positive X inputs values in the X is one what is her out the going to be is then be to to the first power and that is going to simply be two so wise going to be two when X is one okay we're going to be computing one more output value that is the outputs when X is positive to okay let's take a look at on what that one is so when X is positive to write that I have why equals two to the second power okay so to the second power is to times see which is four so outstripped in this case will be four all right let's set up our coordinate system for graphing okay so whenever you want to set up your coordinate system to graph any function you want to take a look at the behavior of the inputs in the output values if you take a look at my in values is spread symmetrically about zero and where from negative to to two so our y-axis we be position right in the center right and if you take a look at output values there are positive so that basically means that from our X axis will be position of the bottom since we looking at any the negative why values okay so let's keep that in mind and go ahead and set up our coordinate system so that the this is my y-axis so that the or is my what my X axes on the position my y-axis right in the center somewhere in the center so you have it even spread between negative two and two okay let's shift our X axes down the little bit because we going to be counting by 4X let's calibrate our x-axis first so 123 is called out one and then 123 all that to that's good enough we

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