If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:6:43

CCSS.Math: ,

Carter has noticed a few quantitative relationships related to the success of his football team and has modelled them with the following functions are this is interesting so he has this function which he denotes with capital n is the winning / and the input of it is the winning percentage W and then the output is the average number of fans per game so he's making some type of model it says look the number of fans per game are going to be in some way dependent on what your winning percentage is and I'm assuming his model the higher the winning percentage the more fans are going to show up at a game now this is AB W the input is the average daily practice time X and the output is the winning percentage all right that makes sense probably once again probably some type of a positive effect of practicing more is going to create the winning a higher winning percentage and this other function number of rainy days are and then average practice time yep well the the more rainy days are you have well that's going to lower your average practice time so I guess I definitely see how practice time P would be a function of number of rainy days the expression n of W of X represents which of the following well before we even look at the choices let's think what's happening this is another way of denoting we're going to take X we're going to take X right over here and we are going to input it into W and we're going to get out W of X and then we're going to input that into the function N and we are going to get out n of W of X so what does the function W do what does the dup function W do right over here well that's winning percentage as a function of practice time so you input practice practice time and it gives you what somehow predicts a winning percentage winning percentage and you take that winning percentage and you in put it into function n function n is is going to output the number of fans per game based on winning percentage so this is number of fans so when you take the composite function you're actually creating a function that starts with practice time as the input and shows a number of fans that are going to be dependent on your practice time so this is interesting so we should look for a choice that says how does the number of fans that show up at a game how is that dependent on practice time X all right the team's winning percentage is a function of the average daily practice time now that would be just W of X if they said just W of X that would be winning percentage as a function of average daily practice time so I can I can cross that one out the average number of fans per game this is interesting because that's what the final output is going to be in terms of the average number of fans per game that is the output of the function n the function n right over here the average number of fans per game as a function of the number of rainy days in a season nope we're not doing that we're doing it as a function of practice time you could construct that in fact if you wanted to do this that would be n as a function of W as a function of P of R so that would have been this choice where you input the number of rainy days from that you're able to figure out practice time and then you input practice time to figure out wind percentage and then you input wind percentage to figure out the number of fans in the crowd but that's not what we're doing here we're just starting with we're just starting with daily practice time and getting two fans per game so let me rule this one out and if you found this one a little bit what I just did a little bit confusing I encourage you to try to set up a diagram like I just did in the beginning of saying oh well look we could start with r to get use that as input get average daily practice time and then use that as a input into W to get winning percentage then use that as an input into n to get average number of fans per game but that's not what they're describing for n of W of X the average number of fans per game as a function of the team's average daily practice time yeah that's what's going on you have your average practice time X being inputted into the function W so your average practice time is going in put it into W and it outputs winning percentage which you then input into N and to get the average number of fans per game the average number of fans per game as a function of the team's average daily practice time so yep I definitely like that choice let's do another one of these this is this is interesting deniz studied the park near her home where she identified several quantitative relationships and modeled them with the following functions so be it inputs the height of a tree in terms of X and it outputs the number of birds nesting in that tree H input the average temperature specific location and it outputs the height of the tree at that location and T the altitude of a specific location and then if that's the input and then the output is the average temperature of that location all right this is interesting of course according to Denise's findings which of the following expressions represents the height of a tree as a function of its altitude so we want to figure out we want to output the height of a tree and we want to input the altitude of a specific location so let's think about it if we take our altitude a specific location R and we input it into the function T out of that we're going to get T of our T of me write a little bit neater we're going to get T of R which would represent average temperature of that location average temp and then if we take the average temperature that location and input it into function H and then we input into function H we are going to get the height of a tree at that location so we're going to get H of T of R and so this is going to be height of tree at that location height of tree and so there you have it H of T of R you start with our altitude at a specific location input into function TT is going to spit out the average temperature the location you input that into H it's going to get the height of the tree at that location so H of T of our H of T of R is this choice right over there