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### Course: Get ready for AP® Calculus>Unit 1

Lesson 2: Inputs and outputs of a function

# 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?
• 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.
• For anyone who is confused.

Think of the inputs as mail and the outputs as houses. You can't have the same package going to two different houses. That is why an input can't have two outputs.
Yet 2 packages can go to the same house so that is why two inputs can have one output.

Hope this helps anyone!
• 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
• 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.
• what is the difference between input and output
• 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!
• how much inputs and outputs can there be?
• It depends upon the function. Many functions that are represented using equations will have an infinite set of inputs and outputs.
• Sal says, "they have graphed y = f(x)". What does it actually mean? What about x = f(x).What would that mean?
• 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
• 1 input can't have 2 outputs.But 1 output can have 2 inputs.WHY?
• How much inputs and outputs can there be?
• 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!