Evaluating composite functions: using graphs (video) | Khan Academy (2024)

Want to join the conversation?

Log in

  • Samuel Lee

    7 years agoPosted 7 years ago. Direct link to Samuel Lee's post “Isn't there another way t...”

    Isn't there another way to write g(f(-5))?

    (6 votes)

    • Toluwalase Adetosoye

      a year agoPosted a year ago. Direct link to Toluwalase Adetosoye's post “(g ∘ f)(-5)”

      (g ∘ f)(-5)

      (4 votes)

  • Vivienne_Li

    7 years agoPosted 7 years ago. Direct link to Vivienne_Li's post “sorry, but how did he pic...”

    sorry, but how did he pick where the -2 point would match up on the graph? Looking back, couldn't 4 have had the same chance??

    (8 votes)

    • Ini

      3 years agoPosted 3 years ago. Direct link to Ini's post “You probably don't need t...”

      You probably don't need this now but someone else might so.
      I'm assuming this from when he solved f(-5).
      To get this answer, you use the blue graph which is representing the values of f(x),
      You get -5 on the x-axis and trace it down to where the blue curve intersects the line you traced down
      When you trace the intersection point to the y-axis, you get -2 which is Sal's answer

      (4 votes)

  • •.¸¸.•ᵇᵉˢᵗᶤᵉˢ•._.•

    a year agoPosted a year ago. Direct link to •.¸¸.•ᵇᵉˢᵗᶤᵉˢ•._.•'s post “Are we going to use this ...”

    Are we going to use this our life?

    (0 votes)

    • ellery

      a year agoPosted a year ago. Direct link to ellery's post “As with any "when will we...”

      Evaluating composite functions: using graphs (video) | Khan Academy (10)

      As with any "when will we use this" question, it largely depends on what you're interested in and what careers you want to go into. If you're entering computer science, finance, business, or a math-based field (such as physics or engineering) then yes, this is an important concept to know. If you aren't, then it's still a great thing to learn, but there's no guarantee you will get the chance to use it in the real world.

      (19 votes)

  • Diana C

    5 years agoPosted 5 years ago. Direct link to Diana C's post “What if we do (f+g)(4). H...”

    What if we do (f+g)(4). How do we find that using only the graph?

    (4 votes)

    • CCDM

      4 years agoPosted 4 years ago. Direct link to CCDM's post “Well, I believe you are a...”

      Well, I believe you are asking for f(g(4))...If so, you would look up g(4) from graph and find -2. Then look up f(-2) from graph and see that it is 4 and there you go. Hope this is useful to you...

      (4 votes)

  • Prisha Rai

    5 years agoPosted 5 years ago. Direct link to Prisha Rai's post “At 2:35, how do we get th...”

    At

    Evaluating composite functions: using graphs (video) | Khan Academy (15) 2:35

    , how do we get that g(-2) is equal to one?

    (3 votes)

    • Russell

      5 years agoPosted 5 years ago. Direct link to Russell's post “When you look at the para...”

      When you look at the parabola for g(x), and find the point on that parabola where x = -2, you find that y = 1. So, g(-2) = 1

      (6 votes)

  • JM K

    8 years agoPosted 8 years ago. Direct link to JM K's post “Okay, so all this composi...”

    Okay, so all this composite function things are very neat, but in the mathematical world, where would this come to use?

    (2 votes)

    • Ryan Thammakhoune

      8 years agoPosted 8 years ago. Direct link to Ryan Thammakhoune's post “In some lesson, before, t...”

      In some lesson, before, there was a farming example. It takes crop yield and finds the total profit. Go look at that and think about it.

      (6 votes)

  • Kayla

    5 years agoPosted 5 years ago. Direct link to Kayla's post “How could I apply this to...”

    How could I apply this to a real life scenario?

    (3 votes)

    • CCDM

      4 years agoPosted 4 years ago. Direct link to CCDM's post “Well, lets say you had on...”

      Well, lets say you had one curve which was the cost per item c(x) of producing an agriculturally based product as a function of quantity produced, x. This curve would have a negative slope because generally it costs less per item as you make more of them (efficiency). However, lets say that the quantity produced was also a function of rainfall where say too little and too much rainfall produced low quantities and the curve x(r) was more parabolic shaped at least for a limited domain. You could plug in x(r) for x in c(x) and find the cost per item as a function of rainfall. This is just one example, there are many more...

      (3 votes)

  • Aryleen Garcia

    6 years agoPosted 6 years ago. Direct link to Aryleen Garcia's post “where did you get -5? for...”

    where did you get -5? for f(x)

    (2 votes)

    • birdybella

      6 years agoPosted 6 years ago. Direct link to birdybella's post “He just picked that numbe...”

      He just picked that number randomly for the problem. Any number that could be graphed on the line y=f(x) would have worked just as well.

      (3 votes)

  • jake jin

    5 years agoPosted 5 years ago. Direct link to jake jin's post “given f(x)=-x+6 and g(x)=...”

    given f(x)=-x+6 and g(x)=f(x+3), how to write an equation for function g?

    (2 votes)

    • loumast17

      5 years agoPosted 5 years ago. Direct link to loumast17's post “What does f(x+3) mean? w...”

      What does f(x+3) mean? well if instead you were doing say f(3), how would that look? well f(3) means plug in 3 for wherever there's an x in -x+6. so f(3) = -(3)+6 = 3.

      So f(x+3) means plug x+3 in for x. so f(x+3) = -(x+3)+6 = -x - 3 + 6 = -x+3. So that means g(x) = f(x+3) = -x + 3. I hope this helped.

      (3 votes)

  • Swetha

    a year agoPosted a year ago. Direct link to Swetha's post “Are we trying to find the...”

    Are we trying to find the y value of each function?

    (2 votes)

    • 464967

      a year agoPosted a year ago. Direct link to 464967's post “Technically, yes we are”

      Technically, yes we are

      (2 votes)

Video transcript

- So we have the graphsof two functions here. We have the graph y equals f of x and we have the graphy is equal to g of x. And what I wanna do in this video is evaluate what g of, f of, let me do the f of it another color, f of negative five is,f of negative five is. And it can sometimesseem a little daunting when you see these composite functions. You're evaluating the functiong at f of negative five. What does all this mean? We just have to remind ourselves what functions are all about. They take an input andthey give you an output. So really, what we're doing is we're going to take, we have the function f. We have the function f. We're going to input negativefive into that function. We're going to input negative five into that function andit's going to output f of negative five. It's going to output f of negative five and we can figure what that is. And then that's going to be the input into the function g. So that's going to be theinput into the function g and so we're going to, and then the output is goingto be g of f of negative five, g of f of negative five. Let's just do it step by step. So the first thing we wanna figure out is what is the function f whenx is equal to negative five? What is f of negative five? Well we just have to see whenx is equal to negative five. When x is equal to negative five, the function is right over here. Let's see, let me see if Ican draw a straight line. So then x is equal to negative five. The function is right over here. It looks like f of negativefive is equal to negative two. It's equal to negative two. You see that right over there. So, f of negative five is negative two. And so we can now think of this instead of saying g of f of negative five, we could say well f of negativefive is just negative two, is just negative two. So this is going to beequivalent to g of negative two, g of negative two, g of negative two. We're gonna take negative two into g and we're gonna output g of negative two. So we're taking that output, negative two and we're inputting into g. So when x is negative two, when x is negative two, what is g? So we see, when x is negative two, g, the graph is right over there, g of negative two is one. So this is going to be one. So g of f of negative fivesounds really complicated, we were able to figure out is one 'cause you input negative five into f, it outputs negative two. And then you input negativetwo into g, it outputs one and we're all done.

Evaluating composite functions: using graphs (video) | Khan Academy (2024)

References

Top Articles
Latest Posts
Article information

Author: Aron Pacocha

Last Updated:

Views: 6438

Rating: 4.8 / 5 (68 voted)

Reviews: 83% of readers found this page helpful

Author information

Name: Aron Pacocha

Birthday: 1999-08-12

Address: 3808 Moen Corner, Gorczanyport, FL 67364-2074

Phone: +393457723392

Job: Retail Consultant

Hobby: Jewelry making, Cooking, Gaming, Reading, Juggling, Cabaret, Origami

Introduction: My name is Aron Pacocha, I am a happy, tasty, innocent, proud, talented, courageous, magnificent person who loves writing and wants to share my knowledge and understanding with you.