The 12 Basic Function Parent Graphs (Need to Memorize)

so these are the 12 basic graphs that I want all of my students that are in pre-calculus or calculus to make sure they know you're going to learn them in Algebra 1 Algebra 2 and even you'll get into some in pre-calculus but I think it's really really important when we're talking about Transformations or graphing functions that you know what the parent graph is going to look like so there's 12 basic of them that I need you to make sure you study you understand we'll get into more details of each function in a separate video but you should be able to visualize each and every one of these functions when I say the name the first one is obviously going to be the easiest which is going to be the identity function right we're familiar with this this is going to be just a line that's going to create and a lot of times we talk about those in slope intercept form but the purest way to write that is just going to be as Y is equal to X now the next one we also deal with in Algebra 1 is going to be our quadratic which is going to be our u-shaped graph this one is very very important to make sure that we use a lot of times we deal with this again for simplifying and solving all the time to find the solutions here then also in Algebra 2 or at least in Algebra 2 we start introducing the absolute value function and that is going to be look very very similar to our quadratic function but again we call this one like the v-shaped graph then the next one that I want to make sure you know is going to be what we call the s-curve graph that is going to be Y is equal to X Cub as we start raising up these Powers these are going to be very very important to our understanding of not just Transformations but how different functions are going to go ahead and interact then we can go and take a look at using some rational powers or using the radicals so the first one be y equal the sare < TK of X and this one is no longer just going to be having going in both directions we're actually going to have an ending point here at the origin and then also we have the cube root of x which is going to look very similar to the square root but it's actually going to be continuous going out in either one of these two directions then you got to make sure these I don't know why students go ahead and get these confused but it's very very important to make sure you understand yal e to X all right all right these are going to have a horizontal ASM toope and then a y intercept at 0a 1 and then we go with the logarithmic function or you can use natural logarithm or logarithm base 10 doesn't really matter in this case but notice that these are going to be two functions that are going to be inverses of each other oops let's forget the X then another one that's really important that is gets confused all the time is going to be the reciprocal function y is equal to 1 /x we know it's going to have a positive component and we know we're going to have a component so we introduce ASM tootes with the exponential the logarithmic and here the reciprocal function is going to have a vertical as well as a horizontal ASM toope I guess I should actually include these going both ways and then once you get into your study of trigonometry we're going to introduce you to the S cosine and tangent and I believe these are critically important for understanding your trigonometric functions because we can do a lot with our understanding not just of like the unit circle and triangles but understanding what the graph looks like can help us be able to Aid in solving problems or just our understanding so the first one is going to be a s of X now it's important that these graphs are going to continue so I'm just going to go ahead and do a quick little period of in the beginning in the front and do kind of the same thing over here that's going to be the cosine of x and then we have y is equal to the tangent of X and that is going to be kind of look similar to the S curve and it's going to be continuous there's infinite many periods that are going to the positive and negative Direction and notice one thing these are all going to be continuous functions these are the functions that I focused on in my class if you're into discrete mathematics then we can do a honorable mention for the step function that shows up a lot of times but in this video I wanted to focus on our continuous functions and we'll get into more details on each of these coming up in the next video