That is simply a result of the definition of a function. A function is a mapping such that for each value of x there is only one value of y.
points
Test it by the vertical line test. That is, if a vertical line passes through the two points of the graph, this graph is not the graph of a function.
The function is not continuous.
We set the denominator to zero to find the singularities: points where the graph is undefined.
The function y = x is the graph that passes from the points (-1, -1), (0, 0), and (1, 1) The function y = 4x is the graph that passes form the points (-1, -4), (0, 0), and (1, 4) Sketch these graphs in a same x and y coordinate system, and you can see both of them
You find the average rate of change of the function. That gives you the derivative on different points of the graph.
points
Test it by the vertical line test. That is, if a vertical line passes through the two points of the graph, this graph is not the graph of a function.
The vertical line test can be used to determine if a graph is a function. If two points in a graph are connected with the help of a vertical line, it is not a function. If it cannot be connected, it is a function.
If a vertical line, within the domain of the function, intersects the graph in more than one points, it is not a function.
If a vertical line, within the domain of the function, intersects the graph in more than one points, it is not a function.
Yes it is possible. The solutions for a quadratic equation are the points where the function's graph touch the x-axis. There could be 2 places to that even if the graph looks different.
The "vertical line test" will tell you if it is a function or not. The graph is not a function if it is possible to draw a vertical line through two points.
Since there are no "following" points, none of them.
The function is not continuous.
They mean the graph/function is decreasing.
A polynomial function have a polynomial graph. ... That's not very helpful is it, but the most common formal definition of a function is that it is its graph. So, I can only describe it. A polynomial graph consists of "bumps", formally called local maxima and minima, and "inflection points", where concavity changes. What's more? They numbers and shape varies a lot for different polynomials. Usually, the poly with higher power will have more "bumps" and inflection points, but it is not a absolute trend. The best way to analyze the graph of a polynomial is through Calculus.