Lucius Romp asked, updated on September 29th, 2021; Topic:
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Mentor: Look at one of the graphs you have a question about. Then take a vertical line and place it on the graph. If the graph is a function, then no matter where on the graph you place the vertical line, the graph should only cross the vertical line once.
Along with it, how do you know if it is a function or not?
A WAY easier (and faster), way to know if it is a function is to see if there are two of the same x-intercept (which make a vertical line). If there is, then it is NOT a function.
Not to mention, how do you tell if a graph is a function or relation? A relation where each element in the domain corresponds to exactly one element in the range. If any vertical line intersects the graph more than once, then the graph does not represent a function. The notation f(x)=y, which reads “f of x is equal to y.” Given a function, y and f(x) can be used interchangeably.
In the overall, how can you identify a function?
How do you tell if something is a function without graphing?
If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function. Using the vertical line test, all lines except for vertical lines are functions.
A function is a relation in which each input has only one output. : y is a function of x, x is not a function of y (y = 9 has multiple outputs). ... : y is not a function of x (x = 1 has multiple outputs), x is not a function of y (y = 2 has multiple outputs).
Defining the Graph of a Function. The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation. Example 1.
A relation has an input value which corresponds to an output value. When each input value has one and only one output value, that relation is a function. Functions can be written as ordered pairs, tables, or graphs.
x=±√y is not a function because for some x input (or in this case almost every x input), there are two different y outputs. x=±√y is still an equation and can still be graphed, but it is not a function. You can have a function x=√y if you refer only to the principal (positive) answer.
if you can draw any vertical line that intersects more than one point on the relationship, then it is not a function. This is based on the fact that a vertical line is a constant value of x, so if there is one input, x, with more than two outputs, y, then it breaks the function rule.