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Worked example: two inputs with the same output (graph)

Sal finds the input value other than -5 for which f(x)=f(-5), given the graph of f.

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  • mr pants teal style avatar for user Jonalie
    So two different inputs can have the same output?
    (5 votes)
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  • blobby green style avatar for user Priyu Pathak
    A function can have same output for more than one input?
    A function can have same input for more than one output
    True or false .justify
    (4 votes)
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    • mr pink green style avatar for user David Severin
      Outputs do not matter when it comes to functions, the definition is that any input can have at most one output (it is possible for an input to zero or one outputs). Thus, the first statement is true because it does not matter about outputs, but the second is false because you need a one on one relationship between input and output.
      (4 votes)
  • male robot hal style avatar for user Daniel Six
    what is the difference between input and output
    (2 votes)
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    • starky tree style avatar for user Saket
      The input is what comes in.. (in this case: the x value). Then comes the process, where the input is processed (in this case: the function), which is self-explanatory, and finally the output, the result of the process (in this case: the y value).
      input --> process --> output

      x --> function --> y

      Hope this (could have) helped!
      (5 votes)
  • male robot donald style avatar for user jumper
    Sal says, "they have graphed y = f(x)". What does it actually mean? What about x = f(x).What would that mean?
    (3 votes)
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    • starky tree style avatar for user shihabdec1312
      y=f(x) is a function relating x and y
      You can say that for a given x value the 'f' gives us the respective y values.So, it cannot be equal to x i.e. x cannot be equal to f(x)
      Check out the topics on functions in Algebra II for better undestanding
      (3 votes)
  • starky ultimate style avatar for user Pranav K
    1 input can't have 2 outputs.But 1 output can have 2 inputs.WHY?
    (3 votes)
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  • male robot donald style avatar for user Jakub
    How much inputs and outputs can there be?
    (3 votes)
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    • duskpin ultimate style avatar for user Cowboy
      For any given function, there are infinite inputs—and if there are infinite inputs, there are infinite outputs... it all depends on what you are looking for when you use a function.
      You see, a function can't necessarily be solved like "A + B = C", you can only plug a number in and see what the function will churn out.
      Hope this explains it a little better!
      (1 vote)
  • duskpin ultimate style avatar for user Sid
    Is there a name for the curved lines on the graph?
    (2 votes)
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    • duskpin ultimate style avatar for user jasminepandit
      The graph is called a function and the highest and lowest points on the graph are called absolute maxima and minima. Points that are comparatively higher or lower are called relative maxima and minima. Some examples of graphs that are curved are hyperbolas, parabolas, exponential graphs, and cardioids.
      (3 votes)
  • aqualine ultimate style avatar for user Haya Aboudan
    so each input can only have 1 output but each output may have more than 1 input
    (2 votes)
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    • starky seedling style avatar for user Aaron Ghosh
      Yes, you are correct. For every input, there is exactly one output, if it is a function. However, there may be more that one of an output, as long as they lead back to different inputs. I realize that this was a bit wordy, so comment on this if it does not make sense. Hope this helps!
      (1 vote)
  • blobby green style avatar for user tvalladares
    this problem confused me. the wording in the question. how are those two values even equal? i would have never figured that out on my own.
    (2 votes)
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  • blobby green style avatar for user shmur425
    What is a function piece to show the cost for grooming a dog if the cost is $35 for 15 pounds and under
    (2 votes)
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Video transcript

The graph of the function f is shown below. What is the input value other than negative five for which f of x is equal to f of negative five? So, we have our x axis, we have our y axis. And then in blue, they've graphed y equals f of x. So for example when x is equal to one, f of x, when y is going to be equal to f of x --that's what this graph is-- f of x is equal to one. When x is equal to seven, f of seven, we see, is equal to five. When x is equal to nine, we see that f of nine is equal to six. So what is the input value other than negative five for which f of x is equal to f of negative five? So, let's see. If x is equal to negative five, f of negative five is... -- we move up here to the graph-- It is equal to four. Cause this, once again, is the graph y is equal to f of x. So the y coordinate here, this is what f of x, this is what five of negative five is equal to. So f of negative five is equal to four. So where else does that happen? So let's see. Let's just move horizontally to the right. That happens here as well. So what input do we have to give? What's the x coordinate here to get y is equal to f of x or f of x is equal to four right over here? Well, we see the x coordinate is also four. So this tells us that f of four is equal to four, which is the same thing as f of negative five. So when x is four, the function takes on the same value as when x is negative five. So x equals four. And we are done.