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Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.
Any equation where variable a = some multiple of variable b2 + constant will graph a parabola.
Normally the input is on the horizontal axis and the output on the vertical axis.
Since the function depends on 4 variables (assuming that p and P are the same variable), the full graph would require 5 dimensions. You can, however, graph something like a cross-section for the graph, in the sense that you keep most of the variables constant, and study the dependency of the function on a single variable at a time.
You cannot.
Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.
A graph represents a function if and only if every input generates a single output.
Any equation where variable a = some multiple of variable b2 + constant will graph a parabola.
Usually x (independent) variable is the input and y (dependent variable) is the output.
Usually x (independent) variable is the input and y (dependent variable) is the output.
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
the output of the function which is graphed
Normally the input is on the horizontal axis and the output on the vertical axis.
Range
A function can only have one output for any given input. This means that any x value you choose cannot have multiple corresponding y values. The vertical line test involves looking at a graph and drawing vertical lines over it. If any of the vertical lines you have drawn touch the graph of the function more than once, then the graph does not represent a function.
The wording is confusing, as a quadratic function is normally a function of one variable. If you mean the graph of y = f(x) where f is a quadratic function, then changes to the variable y will do some of those things. The transformation y --> -y will reflect the graph about the x-axis. The transformation y --> Ay (where A is real number) will cause the graph to stretch or shrink vertically. The transformation y --> y+A will translate it up or down.