Chapter II Functions (Attached Drawings)

Attached:

First, the common solution of function domain:

1, the denominator of the fraction is not equal to zero; 2. The number of even roots is greater than or equal to zero; 3. The real number of logarithm is greater than zero; 4. The bases of exponential function and logarithmic function are greater than zero and not equal to1; 5, trigonometric function tangent function? Medium? ; Cotangent function? Medium; 6. If the function is an analytical formula determined by the actual meaning, its value range should be determined according to the actual meaning of the independent variable.

Second, resolution function's common solution:

1, define the method; 2. Alternative methods; 3. undetermined coefficient method; 4. Function equation method; 5. Parameter method; 6. Matching method

Three, the common solution of function range:

1, substitution method; 2. Matching method; 3. Discrimination method; 4. Geometric method; 5. Inequality method; 6. Monotonicity method; 7. Direct instruction

Four, the common methods to find the maximum value of the function:

1, matching method; 2. Alternative methods; 3. Inequality method; 4. Geometric method; 5. Monotonicity method

Five, the common conclusion of monotonicity of function:

1, if? So, are all the increase (decrease) functions in an interval? It is also an increase (decrease) function of this interval.

2. What if? Is an increase (decrease) function, then? Is a decreasing (increasing) function.

3. What if? With what? Monotonicity is the same, then? Is to increase the function; What if? With what? Monotonicity is different, and then what? Is a subtraction function.

4. Odd functions have the same monotonicity in symmetric intervals, while even functions have the opposite monotonicity in symmetric intervals.

5. Monotonicity solution of common functions: size comparison, domain evaluation, maximum value, inequality solution, inequality proof and function image making.

Six, the common conclusion of function parity:

1, if a odd function is here? So where is the definition? What if a function? Both odd and even functions. (otherwise)

2. The sum (difference) of two odd (even) functions is an odd (even) function; The product (quotient) of is an even function.

3. The product (quotient) of odd function and even function is odd function.

4. Two functions? And then what? As long as one of them is an even function, the composite function is an even function; When both functions are odd function, the composite function is odd function.

5, if the function? The domain of is symmetric about the origin, then? Can be expressed as. The characteristic of this formula is that the right end is the sum of a odd function and an even function.