When it comes to talking about the structure or content of the AP pre-calculus exam, I personally wouldn't listen to all the middle-aged men online talking about it. Not because anything they are saying is wrong or anything, but because they didn't take the exam. Do you want to know who actually did take the AP pre-calculus exam? Me. That's right. Today, I am finally listening to my comment section and making an FRQ review video for the first FRQ. AP pre-calculus is a unique AP exam in its ways because on the F FRQs, it literally tells us exact topics you will be assessed on in different FRQs and sometimes it even tells us outright what the exact questions will be. So with this in mind, let's talk about FRQ1. This is one of the F FRQs that requires you to have a graphing calculator. For this F FRQ, the question will start out by giving you either a graph, table, or equation. Then it will give you three parts to solve for this graph, table, or equation, and it will ask you questions on them. And in case you're wondering, yes, we do know what these questions will be. They could be chosen from six topics. Function composition, inverse functions, input output values, zeros, and behavior, and predicting function models. And I hate to self-promote or anything. Hell, who am I kidding? Each of these topics already have videos on this channel associated with them. I recommend watching them to remind you all of each of them and their content. And as much as I would love to end the video here, I probably should go to the AP exam I took in 2024 and do the F FRQ1 they gave me. So, let's do it together. And look at that. They give us a graph. I'm going to try and read this in my most middle-aged voice. The fig the the figure the figure shows the graph of the function f on its domain of -3.5 to positive 3.5. The points -3a 1 0 comma 1 and 3a 1 are on the graph of f. The function g is given by g ofx= 2.916 * 0.7 to the x. So we are actually given a graph and an equation here. So let's do some labeling. The f function is the graph and the g function is the equation. Now let's read the a part. The function h is defined by h ofx= g of f ofx or g of f ofx. Find the value of h of 3 as a decimal approximation or indicate that it is not defined. When we are given something like this, we start from the inside and go to the outside. Since three is on the inside and f is on the inside of g, we need to find first what f of 3 is equal to. Looking at the graph, f of 3 is equal to 1. So now we find g of 1. So we plug one into the g equation and after plugging this into our calculator, we get 2.041. That means h of 3 is equal to 2.041. Cool. Now let's keep going and read over the next one. Find all values of x for which f ofx is equal to 1 or indicate that there are no such values. Hey look, an easy equation. So we are looking at what x values y = 1 at on our graph. We see this in three spots. x= -3, x= 0, and x= 3. And on to the next part. Find all values of x as decimal approximations for which g of x is equal to 2. Or indicate that there's no such values. All right. So there's two ways you could do this. The first is that you could go on your calculator and plug the g equation into your y equals and plug in two as another value on your y equals. Then on any intersection points you find, the x value of it will be your answer. Or you could do it algebraically and start by plugging in two for y. Then divide the 2.916 from each side. Then rearrange it into log form. We get log base 0.7 of 2 / 2.916. Plug that into your calculator and solve. Whether you do method 1 or two, you will get the same answer of x = 1.057. All right, next one. Determine the end behavior of g as x increases without bound. Express your answer using the mathematical notation of a limit. We see that g is an exponential decay function because b is between 0 and 1 being 0.7. If you remember from my 2.3 video, the end behavior of an exponential decay function is this. And since we are talking about when x increases without bound, we are talking about this one. I'm telling you, man, this is why it's important to watch my videos. Or you could just graph the g function on your calculator and use the graph to graph the end behavior. But I like my weight better. All right, C part. Let's go. Determine if f has an inverse function. Remember that a graph has an inverse function if it is one one by passing the horizontal line test. Looking at the f graph it does not pass the test. So quick answer we say no. Now for the next question give a reason for your answer based on the definition of a function and the graph y= f ofx. Now here is where we get fun. Let me give you some quick answers that you do not give here. Do not say something like f is not 1 one or f does not pass the horizontal line test because if you choose these answers it will not give you a point for this question. Remember what I said in my topic 2.8 video for a graph to have an inverse function each output value is produced by exactly one input value. We see here that the output value of one does not produce one input and rather produces three inputs at -3 0 and 3. So for our explanation, we could put something like f does not have an inverse function because the output value one has more than one input value mapped to it. And this explanation will give us full points. And there we go. We have solved FRQ1. I should mention that even if you don't get the answer right to one of these problems, College Board will give you partial credit on some of the questions as long as you show your work, which could even be the difference between a three and a four or a four and a five. And sometimes they won't even give you any points if you show no work, even if you get the question right. So, make sure you show all your work on all problems in the space they give. Hey, and thanks for sticking around and watching me ramble. I know this was not an under threeminute video, but honestly, I couldn't be asked to make one of the scripts. Why don't you watch this video and subscribe to this channel and have a look at my Instagram if you get the chance. Thank you all.