The first volume (multiple choice questions ***60 points)
First, multiple-choice questions (this big question * * 10 small questions, 5 points for each small question, ***60 points)
1. Given A={x|y=x, x∈R}, B={y|y=x2, x∈R}, then A∩B is equal to.
A.{x|x∈R} B.{y|y≥0}
C.{(0，0)，( 1， 1)} D。
2. The solution set of equation x2-px+6=0 is m, the solution set of equation x2+6x-q=0 is n, and M∩N={2}, then p+q is equal to.
2 1
3. Among the following four functions, the one that is increasing function on (0, +∞) is.
A.f(x)=3-x B.f(x)=x2-3x
C.f(x)=- D.f(x)=-|x|
4. If the function f (x) = x2+2 (a- 1) x+2 decreases (-∞, 4) in the interval, then the range of a is
A.と-3，+∞b .(-∞，-3)
C.(-∞，5〔d .〕3，+∞)
5. Among the following four functions, y=x represents the same function.
A.y=( )2 B.y= C.y= D.y=
6. The inverse function of the function y=+1(x≥ 1) is
a . y = x2-2x+2(x < 1)b . y = x2-2x+2(x≥ 1)
c . y = x2-2x(x < 1)d . y = x2-2x(x≥ 1)
7. Assume that the definition domain of the function f(x)= is all real numbers, and the range of m is
A.0 & ltm≤4 B.0≤m≤ 1 C.m≥4 D.0≤m≤4
8. A shopping mall implements preferential shopping activities for customers, and stipulates a total payment for shopping:
(1) No discount if it does not exceed 200 yuan;
(2) More than 200 yuan dissatisfied with 500 yuan, 10% off the marked price;
(3) If it exceeds 500 yuan, 500 yuan will be given preferential treatment according to Article (2), and the part exceeding 500 yuan will be 30% off.
Someone went shopping twice and paid 168 yuan and 423 yuan respectively. Suppose he buys the same goods twice, and the accounts payable are
A 4 13.7 yuan B 5 13.7 yuan
C 546.6 Yuan Ding 548.7 Yuan
9. Images with quadratic function y=ax2+bx and exponential function y=( )x can only be
10. If the function f(n)= where n∈N, then f(8) is equal to.
A.2 B.4 C.6 D.7
1 1. as shown in the figure, let a, b, c, d>0, and it is not equal to 1, y=ax, y=bx, y=cx, y=dx in the same coordinate system as shown in the figure, then the order of a, b, c and d is.
a、a & ltb & ltc & ltd B、a & ltb & ltd & ltc
c、b & lta & ltd & ltc D、b & lta & ltc & ltd
12 ... Known 0
A. the first quadrant; B. the second quadrant; C. the third quadrant; D. the fourth quadrant
Volume 2 (70 points for non-multiple choice questions * *)
2. Fill in the blanks (4 small questions in this big question, 5 points for each small question, 20 points for * * *)
13. It is known that f (x) = x2- 1 (x
14. The domain of this function is _ _ _ _ _ _ _ _ _ _
15. The functional relationship between the output y of a product in a factory in the past 8 years and the time t years is as follows:
① The growth rate of total output in the first three years is getting faster and faster;
② The growth rate of total output in the first three years is getting slower and slower;
(3) After the third year, stop producing the product;
After the third year, the annual output of this product will remain unchanged.
The correct one in the above statement is _ _ _ _.
16. The maximum value of the function y= is _ _ _ _ _ _.
Third, answer questions.
17. Find the maximum and minimum values of the function y= interval [2,6]. (10)
18. (The full mark of this small question is 10) Try to discuss the monotonicity of the function f (x) = loga (a > 0 and a≠ 1) and prove it.
answer
I. BACCB BDCAD BA ii. 13.2,14.,15.① ④16.④
3. 17. Solution: Let x 1 and x2 be any two real numbers in the interval [2,6], and x 1
f(x 1)-f(x2)= -
=
= .
by 2； 0，(x 1- 1)(x2- 1)>0,
So f (x 1)-f (x2) >: 0, that is, f (x1) >; f(x2)。
So the function y= is the decreasing function on the interval [2,6].
Therefore, the function y= obtains the maximum and minimum values at the two endpoints of the interval, that is, when x=2, ymax = 2；; When x=6, ymin=.
18. solution: let u= and choose x2 > x 1 > 1, then
u2-u 1=
=
= .
∵x 1> 1,x2> 1,∴x 1- 1>0,x2- 1>0.
And ∵ x 1 < x2, ∴ x 1-x2 < 0.
∴ < 0, namely U2 < u 1.
When a > 1, y=logax is increasing function, ∴ logau2 < logau 1,
That is f (x2) < f (x1);
When 0 < a < 1, y=logax is a decreasing function, ∴ logau2 > logau 1,
That is, f (x2) > f (x 1).
To sum up, when a > 1, f(x)=loga is a decreasing function at (1, +∞); When 0 < a < 1, f(x)=loga is a increasing function at (1, +∞).