How many elements are there in the set of values ​​of the quadratic function y=x²+4?

There are several sets composed of the function values ​​​​of the quadratic function y x square 4

1. Quadratic function y=x^2-4 (Note: x^2 represents the square of x)

The independent variable x of the function can take any real number. For any real number x, x^2>=0. When x=0, take the equal sign, then y>=-4

So the set of function values ​​is {y│y>=-4, y is a real number};

2. The inverse proportional function is y=2/x, right?

Recall the image of the inverse proportional function, you can know that the independent variable x can be any real number except 0, and the function value is a non-zero real number. In short, the set of function values ​​is {y│y≠0, y is a real number}.

3. Solution set of inequality 3X>=4-2X

When expressing the inequality 3x >= 4 - 2x as a set, it can be simplified to {x | x >= 4/5}. This set contains all x values ​​that satisfy the inequality.

A collection is a collection of distinguishable objects into a whole. These objects are called elements of the set.

Some specified objects are gathered together to form a collection.

For example, the question above actually means putting numbers that meet certain conditions together to form a set.

Suppose the function y 2x cubed 6x squared 18x7 is the monotonic interval of the concave and convex interval pole

Solution: y=f(x)=2x^3-6x^2-18x-7

f'(x)=6x^2-12x-18=6(x-3)(x 1)=0

The solution is x1=3,x2=-1

When x≤-1, f'(x),≥0, so it is a single increasing interval;

When -1

When x>3, f'(x)>0, so it is a single increasing interval.

f''(x)=12x-12=12(x-1)

f''(x)=0 solves x=1, then point (1,-29) is the inflection point.

When x≤1, f''(x)≤0, so it is a convex interval;

When x>2, f''(x)>0, so it is a concave interval.

f''(3)=24>0,f''(-1)=-24

So f(3)=-61 is the minimum value point, and f(-1)=3 is the maximum value point.

If you don’t understand, please ask.

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