Q: What do you use to determine whether a graph shows a function?

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It shows whether, and how steeply, the terrain or function is increasing or decreasing.

is shows the point where a graph crosses the y-axis

A pie graph shows parts of a whole

Line Graph

You can determine one variable from the other at any given point for that motion, and differentiating the graph gives you the speed at any selected point. You can do this without the plot itself but a graph shows the relationship clearly and immediately.

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It shows whether, and how steeply, the terrain or function is increasing or decreasing.

is shows the point where a graph crosses the y-axis

The slope of each point on the line on the graph is the rate of change at that point. If the graph is a straight line, then its slope is constant. If the graph is a curved line, then its slope changes.

This question appears to relate to some problem for which we have no information. The graph of an exponential function shows a doubling at regular intervals. But we are not told what the role is of b, so we cannot comment further.

For example, if the slope at a certain point is 1.5, you can draw a line that goes through the specified point, with that slope. The line would represent the slope at that point. If you want to graph the slope at ALL POINTS, take the derivative of the function, and graph the derivative. The derivative shows the slope of a function at all points.

a pie graph shows percentages and a bar graph shows numbers and amounts

A pie graph shows parts of a whole

A sigmoid is a mathematical function that is shown on a curve. It essentially shows data on a graph or chart but only ends up showing that data in the shape of an S.

Line Graph

You may mean, what is the graph of the function y = x^2 + 3. This graph shows a upward parabola with a y-intercept of 3 and a minimum at x=0.

a graph law graph shows the relationship between pressure and volume

You can determine one variable from the other at any given point for that motion, and differentiating the graph gives you the speed at any selected point. You can do this without the plot itself but a graph shows the relationship clearly and immediately.