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The integral of a given function between given integration limits will always be a constant. The integral of a given function between variable limits - for example, from 0 to x - can only be a constant if the function is equal to zero everywhere.

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There are infinitely many possibilities which depend on the value of the constant and the constraints and also on whether the required function is linear of not.

Q: How can I generate a declining function with constraints on the x and y intercepts so that the integral of the curve is constant?

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The cosecant function, being defined as 1÷sin(x), has no x intercepts. It has y intercepts at ±∞. (infinity and -infinity)

There is no fixed limit. A periodic function, such as the sine function, can have an infinite number of x-inercepts.

Assuming it is a function of "x", those are two different names for the same thing.

The y-intercept is the value of the function when 'x' is zero. That is, it's the point at which the graph of the function intercepts (crosses) the y-axis. The x-intercept is the value of 'x' that makes the value of the function zero. That is, it's the point at which 'y' is zero, and the graph of the function intercepts the x-axis.

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Yes. A quadratic function can have 0, 1, or 2 x-intercepts, and 0, 1, or 2 y-intercepts.

If the quadratic function is written as ax2 + bx + c, then it has no x-intercepts if the discriminant, (b2 - 4ac), is negative.

The cosecant function, being defined as 1÷sin(x), has no x intercepts. It has y intercepts at ±∞. (infinity and -infinity)

The greatest possible number of intercepts is: 2 of one axis and 1 of the other axis.The smallest possible number of intercepts is: One of each axis.

5x²=0 X=0 the function y=5x² only intercepts x when x = 0

If the problem is 2x^2+11x+12, then it has 2 x-intercepts. (Correct On Apex)

Only if the discriminant of its equation is greater than zero will it have 2 different x intercepts.

There is no fixed limit. A periodic function, such as the sine function, can have an infinite number of x-inercepts.

One.

You can easily identify the x-intercepts of a graph of a quadratic function by writing it as two binomial factors! Source: I am in Algebra 2 Honors!

Assuming it is a function of "x", those are two different names for the same thing.

set the values of the y equal to zero