Q: How can you tell by looking at the graph of a function that it is nonlinear?

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To be linear, there should only be constants, and variables with constant coefficients. No powers of variables, or numbers raised to the power of a variable, or any other nonlinear function such as log, ln, sin, cos, tan, cosh, etc.

You cannot.

If you can differentiate the function, then you can tell that the graph is concave down if the second derivative is negative over the range examined. As an example: for f(x) = -x2, f'(x) = -2x and f"(x) = -2 < 0, so the function will be everywhere concave down.

The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.

For a 2-dimensional graph if there is any value of x for which there are more than one values of the graph, then it is not a function. Equivalently, any vertical line can intersect the a function at most once.

Related questions

To be linear, there should only be constants, and variables with constant coefficients. No powers of variables, or numbers raised to the power of a variable, or any other nonlinear function such as log, ln, sin, cos, tan, cosh, etc.

if a certain abscissa corresponds to more than one ordinate, then it is not a function.

You cannot.

Draw a graph of a given curve in the xoy plane. Now draw a vertical line so that it cuts the graph. If the vertical line cuts the graph in more than one ordinate then given graph is not a function. If it cuts the graph at a single ordinate such a graph is a function.(is called vertical line test)

sine graph will be formed at origine of graph and cosine graph is find on y-axise

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.

If you can differentiate the function, then you can tell that the graph is concave down if the second derivative is negative over the range examined. As an example: for f(x) = -x2, f'(x) = -2x and f"(x) = -2 < 0, so the function will be everywhere concave down.

The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.

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.

For a 2-dimensional graph if there is any value of x for which there are more than one values of the graph, then it is not a function. Equivalently, any vertical line can intersect the a function at most once.

Verticle line test man. If it intersects two points it is its not a function. if it hits one point it is a function. and im currently looking up to see how it is a equation...

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.