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Worked example: Evaluating functions from graph

Evaluating a function at x=-1 using the graph of that function. Created by Sal Khan.

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  • leaf blue style avatar for user Abu Backer Sayeed
    can anyone please tell me what would be the answer of
    f : x > x^2 -5x

    a) find the value of f(-2)
    b) find the value of ff(2)
    c) find the range of f if domain is {-1, 0, 1}

    it would be really grateful of you
    (6 votes)
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    • mr pink green style avatar for user David Severin
      f(x)> x^2 - 5x so by substitution,
      a) f(-2) > (-2)^2 - 5(-2) 4 - (- 10) = 14
      f(-2)> 14
      b) f(2) > (2)^2- 5(2) 4-10 = -6
      f(2) > -6
      c) f(-1) > (-1)^2 -5(-1) f(-1)> 6
      f(0) > 0^2 - 5(0 f(0) > 0
      f(1) = (1)^2 -5(1) f(1) > -4
      I have not seen this type of problem with limited domain with inequality, but
      since the range is the f(x),
      my best guess on how to write it would be {f(x)>6, f(x)>0, f(x)>-4}
      (5 votes)
  • blobby green style avatar for user Sterling Holmes
    I don't understand something. When asked to find f(x), what am I being asked to find? Where do I look to find it?
    (4 votes)
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  • spunky sam red style avatar for user Sujesh Devdassahastrabuddeheshanticurry Ramkrishnabhagawan
    Why is it always f(x) and not any other letters?
    (2 votes)
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    • mr pink green style avatar for user David Severin
      Wait until you get to Algebra 2 when you have to start combining multiple functions, you will start seeing g(x), h(x) etc. In Algebra I, you are just getting used to functional notation, but the power of functional notation over y= form will come later.
      (4 votes)
  • piceratops seedling style avatar for user jsrodriguez
    What if the function is f(-3) but there’s two points going vertically thru -3
    (4 votes)
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    • female robot grace style avatar for user loumast17
      Then it is not a function. A function can only have one y value for every x value. Important to remember there can be multiple x values for a single y value. Kind of confusing but important to remember. if you know it, the vertical line test will tell you if something is a function.
      (4 votes)
  • blobby green style avatar for user rebpap2911
    I do not get this at all I have a test in a few days, this is SO complicated. I need some help. PLEASE HELP ME
    And please answer fast
    (3 votes)
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    • duskpin ultimate style avatar for user shaposhnikovd
      I know this isn't really a fast answer, but,
      basically he is just saying that when the x coordinate is at -1, the y coordinate is 6 on the line.
      He just wants you to find out the y coordinate by using the line, when x (F) is given to you.
      Reply if you actually read this. you probably already got it, but ill write this anyway.
      (1 vote)
  • blobby green style avatar for user lotuswells999
    How to graph a Parabola
    (2 votes)
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    • starky seedling style avatar for user Aaron Ghosh
      A Parabola could be graphed when given the following skeleton equation: ax^2+bx+c. However, it is not easy to explain how to graph parabolas over comments, so it would be much wiser to follow MyAnchorHolds' suggestion and view the videos on Khan Academy.
      (2 votes)
  • leaf green style avatar for user acealena
    Can I write the function as f=x+1?
    (2 votes)
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  • starky sapling style avatar for user ChapinTrinity827
    id love to ask a question, how am I SUPPOSED to know that the grid point of x=4 will make the y plot equal 1 when its NOT STATED?
    I'm sorry, but I am quite frankly wondering how I'm supposed to know that the plot you wanted me to use is (4,1)?? you listed that 4=x, GREAT, but that Y value could be ANYTHING ON THE GRAPH, how am I supposed to know that I'm supposed to use (4,1)? how?
    (2 votes)
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  • mr pants purple style avatar for user josiahfair
    why is it always fx
    (1 vote)
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    • stelly blue style avatar for user Kim Seidel
      Functions are not always f(x). It just happens to be the most frequently used. A function can be names by an letter. And, the input variable doesn't have to be "x" either. It is quite common if a function has a input that is time, to see the letter "t" used instead of "x".
      (4 votes)
  • blobby green style avatar for user Martin Ngugi
    in a graph of y-f(x) what is the value of y=(0)
    (2 votes)
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    • leaf orange style avatar for user A/V
      Drawing a line of x=0 (as you are finding what is f(0)), the intersection point is at (0,8), so 8 is your answer.

      btw just remember that formatting matters and it's f(0) (function of 0) instead of y=0 cause they mean different things.

      hopefully that helps !
      (2 votes)

Video transcript

The function f of x is graphed. Find f of negative 1. So this graph right over here is essentially a definition of our function. It tells us, given the allowed inputs into our function, what would the function output? So here, they're saying, look, what gets output when we input x is equal to negative 1? So x equals negative 1 is right over here. x is equal to negative 1. And our function graph is right at 6 when f is equal to negative 1. So we can say that f of negative 1 is equal to 6. Let me write that over here. f of negative 1 is equal to 6.