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Q: What is the only type of line that is not a function?

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When graphing functions, an inverse function will be symmetric to the original function about the line y = x. Since a constant function is simply a straight, horizontal line, its inverse would be a straight, vertical line. However, a vertical line is not a function. Therefore, constant functions do not have inverse functions. Another way of figuring this question can be achieved using the horizontal line test. Look at your original function on a graph. If any horizontal line intersects the graph of the original function more than once, the original function does not have an inverse. The constant function is a horizontal line. Under the assumptions of the horizontal line test, a horizontal line infinitely will cross the original function. Thus, the constant function does not have an inverse function.

A line. The derivative of a function is its slope. If the slope is a constant then the graph is a line.

use the horizontal line text, a horizontal line intersects the graph of x3 -3 only once so it is one to one.

The asymptote is a line where the function is not valid - i.e the function does not cross this line, in fact it does not even reach this line, so you cannot check the value of the function on it's asymptote.However, to get an idea of the function you should look at it's behavior as it approaches each side of the asymptote.

A linear equation

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It is a straight line equation.

A linear function. It is a horizontal line at -7.

A monotonic, or one-to-one function.

Vertical line. If you can draw a vertical line through some part of a graph and it will intersect with the graph twice, the graph isn't a function.

f(x) = x2 This is a function by the vertical line test because a vertical line drawn through this function will only intersect the function at one point

No. Function overloading only pertains to the type of parameters.

If a vertical line passes through the supposed function at only one spot then you have a function.

No

A function can never be a vertical line, because it then fails the definition of a function: every x value outputs only 1 y value. The vertical line test will determine if a relation is a function. If a vertical line intersects the graph of the function at more than one place, it is not a function.

It is a linear function. That is to say, it is a function representing a straight line in the coordinate plane.

By doing a vertical line test. If you can draw a vertical line and it only passes through the graph once, its a function. If it passes through twice, it is NOT a function.

It is a continuous function. If the line is a straight line, it is a linear function.

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