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Answer:
A) A function is a rule that assigns one input into one output.
The general function is f(x) = y
Where we have one input, x, and one output, y.
But this is a really simple type of function, for example, you could define a function that calculates the volume of a box of length L, width W, and height H as:
V = f(L, W, H) = L*W*H
Then we have "3 inputs" and one output, right?
Well, not exactly, here the set (L, W, H) is called the input, so here we have a single input consisting of 3 variables.
Also we can have functions with a single input into vector-like outputs
For example:
(y, z) = f(x)
So for the input x, we got two values in the output y and z, but this is a single output defined as (y, z), then we always have a single output.
B) The graph of a function is a set of points consisting of one input and the corresponding output.
C) You can determine if a graph represents a function by using the vertical line proof.
A rule that assigns inputs into outputs is only a function if each input is assigned into only one output.
Then if we draw a vertical line that intersects our graph, it should intersect it only one time for functions.
If the line intersects the line two times this means that a single input has more than one output, then this is not a function.
Answer:
A) A function is a rule that assigns exactly one output to each input
B) The graph of a function is a set of ordered pairs consisting of one input and the corresponding output
C) You can determine if a graph represents a function by using the vertical line test
Step-by-step explanation: