Depends on the sort of graph. Time is common is be on the x axis. Frequency may be fro a Power Spectrum Density Function.
The main way that a graph can be defined as a function is if it passes the vertical line test; this means that each individual x must correspond to one specific value of y. In the situation you mentioned, we don't know if the graph in question really is a function, because we only see the point at y; we don't know if the graph loops around on itself and fails the vertical line test at any other point.
Yuo cannot include a graphical illustration here. Take a look at the Wikipedia, under "exponential function" and "logistic function". Basically, the exponential function increases faster and faster over time. The logistics function initially increases similarly to an exponential function, but then eventually flattens out, tending toward a horizontal asymptote.
I'm not sure what exactly you're asking about, but if you're asking about the difference between relations and functions, here's the answer.In a relation, a value in the domain may have one or more values in the range. That is, for every x on graph there may be more than one value of y. In terms of word problems and such, x is the independent variable (i.e. time) and y is the dependent variable (i.e. temperature). Basically, if you graph a relation, you can draw a vertical line anywhere on the graph and that line may intersect one or more points on the graph. A circle or a horizontal parabola is a relation, not a function.In a function, for every value in the domain there is only one value in the range. That is, for every value of x there is one and only one value of y. If you draw a vertical line anywhere on the graph of the function, it will only intersect the graph once. If it intersects the graph more than once, then that graph is not a function. An example of a function would be a vertical parabola, a line, or a cubic.Hope that helps.
A speed graph measures the distance devided over time. Acceleration graph measures the change in speed over time.
To find the starting point of a distance vs time graph from a velocity vs time graph and a function, you would integrate the velocity function to find the displacement function. The starting point of the distance vs time graph corresponds to the initial displacement obtained from the displaced function.
That's not correct. If you have a graph of distance as a function of time, the speed is the slope of the graph.
The slope of the speed-vs-time graph is the magnitude of acceleration.
The slope of a line on a velocity-time graph is acceleration.
It's the rate of change of gradient. Or if you have the function of the distance-time graph, it's d2x/dt2.
To solve a problem involving an acceleration vs. time graph, you can find the velocity of the object at different time intervals by calculating the area under the graph. To find the displacement of the object, you can integrate the acceleration function over the given time interval to get the velocity function, then integrate the velocity function to get the displacement function.
The area under the speed/time graph between two points in time is the distance covered during that time.
No, acceleration is the rate of change of velocity with respect to time. It is the derivative of the velocity function, not the slope of the velocity vs. time graph. The slope of the velocity vs. time graph represents the rate of change of velocity, not acceleration.
The slope of a tangent to the curve of a velocity-time graph represents the acceleration of an object at that specific instant in time. A steeper slope indicates a greater acceleration, while a flatter slope indicates a smaller acceleration.
Depends on the sort of graph. Time is common is be on the x axis. Frequency may be fro a Power Spectrum Density Function.
The area under a position-time graph represents the displacement of an object. It is calculated by finding the area between the curve of the graph and the time axis. The units of the area will be in distance units (e.g., meters, kilometers).
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.