Intro to combining functions (article) | Khan Academy (2024)

Become familiar with the idea that we can add, subtract, multiply, or divide two functions together to make a new function.

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  • Junior Murray

    6 years agoPosted 6 years ago. Direct link to Junior Murray's post “For Part 2 evaluating a c...”

    For Part 2 evaluating a combined function, method 1 where did the 2 come from

    (12 votes)

    • Joshua Lee

      4 years agoPosted 4 years ago. Direct link to Joshua Lee's post “We are substituting x=2 i...”

      We are substituting x=2 into the function.

      (3 votes)

  • gabrielalopes2001.GL

    7 years agoPosted 7 years ago. Direct link to gabrielalopes2001.GL's post “where does (-5) come in t...”

    where does (-5) come in the last practice problem?

    (3 votes)

    • Bailey Mitchell

      6 years agoPosted 6 years ago. Direct link to Bailey Mitchell's post “Hello Gabriela. Sorry for...”

      Intro to combining functions (article) | Khan Academy (7)

      Hello Gabriela. Sorry for a late response. You probably understand the question by now, but I'm going to answer for you anyways.

      Basically, the (t) is like an x-value. If a number replaces the (t) then that is your x-value or your input. The letter on the left of the r(t) is your y-value.
      The 'r' in r(t) =..... is your y-value/output. Your 't' is your input/x-value.
      The 'p' in p(t) =..... is your y-value/output. Your 't' is your input/x-value.
      The 'q' in q(t) =..... is your y-value/output. Your 't' is your input/x-value.

      Of course just remember the positions and all because the letters and values changes. Lol.

      In this case p(3) = t + 2 is synonymous for p = 3 + 2. Remember p is synonymous for y. So in this equation it is p = 5.

      In q(3) = t - 1 Remember q is synonymous for y. It is same thing for THIS scenario. Plug in 3 into your x-value or 't'. They are the same thing. So it is q = 3 - 1. q =2

      In r(3) = t. Essentially whatever is r(t) = t. So whatever is t on the left is t on the right. Think of it like (t) =t = r . (x) = x = y. So all the values are 3.

      Now you just plug your answers in the coordinating spots.
      (*Note the last 5 in the equation below is POSITIVE. So is the 3 before. You are just subtracting the two values.)
      5 * 2 * 3 - 5
      10*3 -5......Multiply first 5*2
      30 - 5 ......Again, multiply 10*3
      25.....Then subtract 30 -5
      Your answer is 25.

      Hopefully you and others will understand.

      (15 votes)

  • Christopher M

    6 years agoPosted 6 years ago. Direct link to Christopher M's post “Are these functions like ...”

    Are these functions like functions in programing in which you can write the function beforehand and then call it whenever you want?

    (6 votes)

    • Sujal J.👍

      6 years agoPosted 6 years ago. Direct link to Sujal J.👍's post “Basically yes ,they are. ...”

      Basically yes ,they are. You can create them based on the information given to you and then you can add, subtract, multiply, and divide it. But you don't neccesarily "call" the function rather you input a given value into the function. So they are similar to each other, but not the exact same.

      (5 votes)

  • Amira

    7 years agoPosted 7 years ago. Direct link to Amira's post “How would I solve the equ...”

    How would I solve the equations
    Given f(x)=2x-3 and g(x)=0.5x+4 find f of g of x? [f of g](x)

    (3 votes)

    • Iris Nogueroles Langa

      7 years agoPosted 7 years ago. Direct link to Iris Nogueroles Langa's post “In order to find [f of g]...”

      In order to find [f of g](x), you need to substitute function g(x) into function f(x) (replace the x in f(x) with function g(x)).

      [f of g](x) = 2(0.5x+4)-3 = x+8-3 = x+5

      Therefore, [f of g](x) = x+5

      (8 votes)

  • dhebel612

    7 years agoPosted 7 years ago. Direct link to dhebel612's post “on part 2 evaluating a co...”

    on part 2 evaluating a combined function do you always replace x wit 2 or not becuse i am confused on how they got 2

    (4 votes)

    • Kim Seidel

      7 years agoPosted 7 years ago. Direct link to Kim Seidel's post “Unless the function has a...”

      Unless the function has a restricted domain, you can evaluate the function (including the combined function) for any value of "x". So, you will not always replace x with 2. You can evaluate the new combined function h(x) for any value of x. Sal just happened to use x=2 to demonstrate the process.

      (5 votes)

  • desit241814

    5 years agoPosted 5 years ago. Direct link to desit241814's post “Will this be on the SAT f...”

    Will this be on the SAT for March 9th, 2019?

    (2 votes)

    • Alex

      5 years agoPosted 5 years ago. Direct link to Alex's post “Function combination may ...”

      Function combination may be on the SAT. It depends on the specific SAT given, and we have no way of finding out if it's on the test, but you should prepare for it nonetheless.

      (2 votes)

  • sf49

    8 years agoPosted 8 years ago. Direct link to sf49's post “I dont understand how the...”

    I dont understand how the addition of the functions in problem 3 is 9 shouldnt it be 6?

    (1 vote)

  • KevinHJoe

    5 years agoPosted 5 years ago. Direct link to KevinHJoe's post “for graphing f(3) + g(3)...”

    for graphing f(3) + g(3)
    Why does f(3)=6 and g(3)=3?

    I see no indicator as to why f(3) should = 6

    (1 vote)

    • Ian Pulizzotto

      5 years agoPosted 5 years ago. Direct link to Ian Pulizzotto's post “Graphically, for any func...”

      Graphically, for any function f(x), the statement that f(a)=b means that the graph of f(x) passes through the point (a,b).

      If you look at the graphs of f(x) and g(x), you will see that the graph of f(x) passes through the point (3,6) and the graph of g(x) passes though the point (3,3). This is why f(3)=6 and g(3)=3.

      (3 votes)

  • cpsnarayan

    7 years agoPosted 7 years ago. Direct link to cpsnarayan's post “I am a doing Advanced Alg...”

    I am a doing Advanced Algebra 1 in sixth grade. Does that mean i do algebra 2 in eighth grade?

    (2 votes)

  • Lancelot.Quitian

    7 years agoPosted 7 years ago. Direct link to Lancelot.Quitian's post “Im in Pre Cal right now.....”

    Im in Pre Cal right now...just looking back on Algebra II for the SAT...I got how the first 2 graphs worked...but to then add a parabola in the third question...just confuses me

    (1 vote)

    • V

      7 years agoPosted 7 years ago. Direct link to V's post “Same here, I'm looking ba...”

      Same here, I'm looking back just to refresh my memory.
      It's simple, just find the x-coordinate that it asks you to, in this case a 3
      Then find where the line intercepts to find the y value, which is for the parabola part, a 6, use the y-coordinates and, in this case, add them together, poof, tell me what you get

      (2 votes)

Intro to combining functions (article) | Khan Academy (2024)

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