Math Questions, Senior 1 Pre study Questions, a Senior 1 Math Pre study Textbook Practice Questions

From the known results, -1 is less than or equal to x+1 less than or equal to 1, and the solution is that 2 is less than or equal to x and less than or equal to 0

f(x+1)=x 2+3x-1 (x+1) 2+(x+1)-3, so y=f(x)=x 2+x-3=(x+1 2) 2+11 4When x=-2, take the maximum value of 5

When x=-1 2, take the minimum value of 11 4

The domain of the function f(x+1)=x 2+3x-1 is [-1,1], then the domain of f(x) is [0,2], and.

f(x)=x^2+x-3

So the range is [-13, 4,3].

Hello. f(x) is defined in the domain of -2,0

f(x)=x+x-3 with respect to x=-1 2 symmetry.

Therefore, when x=-2, there is a maximum value of -1

When x=-1 2 is, there is a minimum value of -13 4

The value range is [-13, 4, -1].

Standard answer, correct.

The answer is hopefully satisfying.

The group has you covered.

Let z = x+1, because the range of the original function independent variable x is [-1,1], so the range of z is [0,2].

Because f(x+1)=x2+3x-1

Recipe it: f(x+1)=(x+1) 2+(x+1)-3 and then replace the variable: f(z)=(z) 2+(z)-3 Recipe the equation about z: f(z)=(z+

Since the range of z is [0,2], the range of z+ is: [, so (z+. The range of z+ is: [-3,3].

That is, the value range of the function f is: [-3,3].

This similar question is easy to understand by using the reduction method.

Analyze it according to the image and do it with monotonicity.

According to the trigonometric properties, the axis of symmetry of f(x)=sin(2x+) is 2x+ =k + 2, and according to the condition, x= 8

is the axis of symmetry, then 4+ =k + 2, so =k + 4, again - 0, so k = -1, =-3 4

f(x)=sin(2x-3 4), according to the trigonometric properties, the monotonic increase interval is, 2n - 2<2x-3 4<2n + 2 (can be taken with an equal sign), and the simplification is 2n + 4<2x<2n + 5 4, so the monotonic increase interval of n + 8 is [n + 8, n + 5 8], where n is an integer.

The axis of symmetry is 2x+ 2, 2 4 4

When 1 satisfies - 0, f(x)=sin(2x 2x 2 2 2 increments,

Problem solving 1 Oxygenated acids: sulfuric acid, nitric acid, acetic acid, phosphoric acid Anaerobic acid: hydrochloric acid.

Monoacid: hydrochloric acid, nitric acid, acetic acid Polyacids: sulfuric acid, phosphoric acid.

High boiling point (stable acid): sulfuric acid, phosphoric acid Low boiling point acid: hydrochloric acid, precursor containing nitric acid, acetic acid.

Soluble chai acid: hydrochloric acid, sulfuric acid, nitric acid, acetic acid, phosphoric acid Insoluble acid: silicic acid.

Strong acids: hydrochloric acid, nitric acid, sulfuric acid Weak acids: acetic acid, phosphoric acid.

Problem solving 2 Soluble base: insoluble base: magnesium hydroxide, iron hydroxide.

Strong Huixiao alkali: sodium hydroxide, calcium hydroxide Weak alkali: magnesium hydroxide, iron hydroxide.

Strong electrolytes: sodium hydroxide, calcium hydroxide Weak electrolytes: magnesium hydroxide, iron hydroxide.

Problem solving 3: Insoluble salts CaCO3, Cu2(OH)2CO3, soluble salts NaCl, NaHCO3

Normal salts: NaCl, CaCO3 acid salts: NaHCO3 basic salts: Cu2(OH)2CO3

Sodium: NaCl Carbonate: CaCO3, Cu2(OH)2CO3 Bicarbonate: NaHCO3

Problem Solving 4 CO2 and SO2 belong to acidic oxides 2KOH + CO2 (less) = K2CO3 + H2O KOH + CO2 (foot) = KhCO3

MGO is a basic oxide, 2MGO + H2SO4 = 2H20 + MGSO4

Problem Solving 5 b

Mixture: A substance containing two or more pure substances.

Pure substance: A substance composed of the same substance is called a pure substance, which is further divided into elemental substances and compounds.

Elemental: A pure substance containing only one element.

Compound: A substance composed of two or more elements.

Elemental metal: An elemental substance composed of metallic elements.

Organics: Substances present in organic life, generally containing carbon but not carbonate.

Inorganic compounds: compounds that are not related to the body (a few compounds related to the body are also inorganic compounds, such as water), corresponding to organic compounds, usually refer to compounds that do not contain carbon elements, but include carbon oxides, carbonates, hydrides, etc., referred to as inorganics.

Acid: Cations containing only hydrogen ions talk about masking substances.

Base: Anion contains only hydroxide group examples of substances.

Salts: Substances containing acid ions and metal ions.

2) Oxygenated acid, anaerobic acid.

Monobasic acids, polyacids.

High boiling point is counted as waiter (stable acid), low boiling point is counted.

Soluble acids, insoluble acids.

Strong acid, weak acid.

Elemental: A pure substance containing only one element.

Since f(x) is a quadratic function, let f(x)=ax +bx+cFirst, f(x)+g(x) is an odd function, let this odd function be t(x) so t(0)=0, and g(x)=-x -3

Substituting t(0)=f(0)+g(0)=c-3=0 c=3 f(x)=ax +bx+3

The odd function t(x) has t(1)+t(-1)=0

Substituting yields: t(1)+t(-1)=f(1)+g(1)+f(-1)+g(-1).

a+b+3-4+a-b+3-4

2a-20 a=1 f(x)=x +bx+3 The image opening is upward, and the axis of symmetry is x=-b 2

Discussion in conjunction with image classification).

The axis of symmetry is to the left of -1, that is, when x=-b 2 -1, the b 2 image is obtained when x [-1,2] is minimum x=-1, and substituting f(-1)=1-b+3=1, b=3 2, is true;

When the axis of symmetry is between [-1,2], it is smallest at -1 -b 2 2 b -4 image x = -b 2.

Substitute f(-b 2) = b 4 - b 2 + 3 = -b 4 + 3 = 1 b = 2 2 ( 2 root number 2).

and 2 b -4, 2 2 2, rounded, -2 2 conformed, established;

The axis of symmetry is on the right side of 2, that is, when the edge x=-b 2 2, the b-4 image is obtained when x [-1,2] is minimum x=2, and is substituted for f(2)=4+2b+3=1b=-3 -4, and rounded.

In summary, the value of b is 3 or -2 2.

So f(x)=x +3x+3 or f(x)=x -2 2x+3.

Do you dare to add some points, it's so difficult!

Because bc ef ad ae:eb=m:n, df:

cf=m:n, so in abc eg:bc=ae:

EB+AE=M:M+N in CAD GF:AD=CF:

cf+df=n:m+n

So (m+n)ef=(m+n)[mbc (m+n)+nad (m+n)]=mbc+nad.

When EF is the median line, m:n=1:1 is 2EF=BC+AD to obtain the median line formula.

When cos(2x+faction 4) takes the maximum value of 1, f(x) has a maximum value, so that cos(2x+faction 4)=1, 2x+faction 4=2k faction, x=k faction-faction 8, and the maximum value is 4

When the 2k faction is less than or equal to (2x+faction 4) and less than or equal to 2k faction + faction, cos(2x+faction 4) decreases, and the decreasing interval k-faction 8 is less than or equal to x less than or equal to k faction + 3 8 factions.

Are a and a in your question the same letter or two letters? I don't remember the formula very well, anyway, you first treat 2a as a whole solution, and then you can find the formula in the denominator more simply, but your a really feels like the problem is incomplete.

∵f(x+6)=f(x)+f(3）

f(-3+6)=f(-3)+f(3）

i.e. f(3) = f(-3) + f(3).

f(x) is an even function on r.

f(-3)=f(3)

f(3)=f(3)+f(3)=2f(3)∴f(3)=0

f(x+6)=f(x)+f(3)=f(x)f(x) is a periodic function with period 6.

f(2005)=f(334*6+1)=f(1)= 2

Since f(x) is an even function on r, then f(3) = f(-3).

Let x=-3, we get f(-3+6)=f(-3)+f(3) i.e. f(3)=0

Let x+6=t, then for any x belonging to r there is f(t)=f(t-6)+f(3).

f（2005）=f（2005-6）+f(3)=f（2005-6*2）+2f(3)

f（2005-3*6）+3f(3)=……=f（2005-334*6）+334*f(3)

f(1)+334*f(3)=2

Let x=-3, then f(3)=f(-3)+f(3)=2f(3), so f(3)=0, so f(x+6)=f(x), so f(2005)=f(2005-6 334)=f(1)=2Proof is complete.

Classmate, I'll tell you this. Give me a point.

Natural number: The number that occurs naturally in nature, used for measurement and sorting, such as , .

Positive integer: is a number greater than 0, excluding decimals. For example, , but it is not a positive integer.

Integer: A number that does not include decimals, it includes positive integers, negative integers, and zeros.

Rational numbers: Your own understanding can be understood in this way, that is, a number with a rational basis, for example, a number such as 3 in reality, or 1 3, these are rational numbers, and unjustified numbers, such as pi, the following numbers have no regularity, so they are unreasonable and unfounded numbers, like one-third into decimals, which is a decimal number of infinite circular three, which is a rational and well-founded number, we know that it has always been a circular three, so it is a rational number. Numbers other than infinite non-cyclic decimal numbers are collectively referred to as rational numbers.

Real numbers: They are numbers that exist in reality, which really exist, including rational numbers and irrational numbers, because they all really exist. Negatives, 0s, and integers are included. It is a general term for the number of things that nature has.

Give me extra points. If you don't understand, you can ask me. I often tutor this area, and I have a lot of experience.

Natural Numbers A number used to measure the number of pieces of a thing or to express the order of things. i.e. digital 1, 2, 3, 4 ,......The number represented. Natural numbers start with 1 and follow each other to form an infinite set.

There are addition and multiplication operations in the set of natural numbers, and the result of adding or multiplying two natural numbers is still a natural number, and it can also be subtracted or divided, but the results of subtraction and division may not be natural numbers, so subtraction and division operations are not always true in the set of natural numbers. Natural numbers are the most basic of all the numbers that people know. In order to have a strict logical foundation for the number system, mathematicians in the 19th century established two equivalent theories of natural numbers, the ordinal number theory of natural numbers and the cardinal theory, so that the concepts, operations and related properties of natural numbers were strictly discussed.

Integer sequence.

The number in is called an integer The whole of an integer constitutes an integer set, which is a ring, denoted as z (usually written as a hollow letter z in modern times) The potential of the ring z is Alev 0

A given integer n can be negative (n z-), non-negative (n z*), zero (n = 0), or positive (n z+).

Rational number: A number that can be accurately expressed as the ratio of two integers

For example, 3,,,7 and 22 are all rational numbers

Integers and commonly known fractions are rational numbers, and rational numbers can also be divided into positive rational numbers, 0s, and negative rational numbers

In the decimal representation system of numbers, a rational number is a number that can be expressed as a finite decimal or an infinite cyclic decimal, and this definition also applies in other carry systems, such as binary

All rational numbers form a set, the set of rational numbers, which is represented by the bold letter q, and some modern math books are represented by the hollow letter q

The set of rational numbers is a subset of the set of real numbers, and the related content is seen in the expansion of the number system

A set of rational numbers is a field in which four operations (except 0 for the divisor) can be performed, and for these operations the following laws hold true (a, b, c, etc., all represent arbitrary rational numbers).

An irrational number refers to an infinite non-cyclic decimals.

In particular, it is important to note that infinitely cyclic decimal numbers are often mistaken for irrational numbers.

Waited until high school ==

Real Numbers A number where there is no imaginary part; A general term for rational numbers and irrational numbers.

That is, in all integers greater than 1, there is no other divisor except 1 and itself, and this integer is called a prime number, and a prime number is also called a prime number. This final rule is only a literal explanation. Is it possible to have an algebraic formula in which the value of the algebraic formula substituted is prime when the number represented by a letter is any specified value?

The distribution of prime numbers is irregular and often incomprehensible. For example, are prime numbers, but 301 and 901 are composites.

In an integer, the number divisible by 2 is even, and vice versa, the even number can be represented by 2k, and the odd number can be represented by 2k+1, where k is an integer.