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## Algebra (all content)

### Course: Algebra (all content) > Unit 7

Lesson 2: Inputs and outputs of a function- Worked example: matching an input to a function's output (equation)
- Function inputs & outputs: equation
- Worked example: matching an input to a function's output (graph)
- Worked example: two inputs with the same output (graph)
- Function inputs & outputs: graph

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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.

## Want to join the conversation?

- So two different inputs can have the same output?(7 votes)
- Yes and that is what happens with quadratic functions. If you have y = x^2, then both 2 and negative 2 give you 4, but this is still a function. Or if you have a line with a slope of 0 such as y = 4, all inputs give you the same output of 4.(22 votes)

- 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(5 votes)- 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.(5 votes)

- what is the difference between input and output(2 votes)
- 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!(8 votes)

- 1 input can't have 2 outputs.But 1 output can have 2 inputs.WHY?(4 votes)
- Sal says, "they have graphed y = f(x)". What does it actually mean? What about x = f(x).What would that mean?(3 votes)
- 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)

- how much inputs and outputs can there be?(3 votes)
- It depends upon the function. Many functions that are represented using equations will have an infinite set of inputs and outputs.(2 votes)

- How much inputs and outputs can there be?(3 votes)
- 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)

- 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.(3 votes)
- What it is saying is that -5 is equal to another number on the positive side. Try watching the confusing part again and it will make more sense.(1 vote)

- Is there a name for the curved lines on the graph?(2 votes)
- 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)

- so each input can only have 1 output but each output may have more than 1 input(2 votes)
- 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)

## 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.