Math topic中文

Power functions

graphs of power functions of the form y=axny = ax^{n}, where n=−2,−1,0,1,2,3n = -2, -1, 0, 1, 2, 3, and simple sums of not more than three of these

Practice questions

  1. 1The sketch shows the graph of y=kxay = kx^a. The points A(-2, -0.75) and B(0, -3) lie on the graph. Find the values of kk…
  2. 2Sketch the graph in the spaces below. y=4xy = \frac{4}{x} y=−2x3y = -2x^{3} Hence, state the number of solutions for the equat…
  3. 3y is inversely proportional to the square of x, x>0x > 0. If x is increased by 25%, find the percentage change in y. Answ…
  4. 4The variables x and y are connected by the equation y=2x3−21x2+54xy = 2x^3 - 21x^2 + 54x. Some corresponding values of x and y are g…
  5. 5Complete the table of values for y=x−4x2y = x - \frac{4}{x^2}. Values are given to one decimal place where appropriate. Compl…
  6. 6The variables x and y are connected by the equation y=x35−2x+1y = \frac{x^3}{5} - 2x + 1. Some corresponding values of x and y a…
  7. 7The table shows some values for y=310x3−x+1y = \frac{3}{10}x^3 - x + 1 for −3≤x≤3-3 \le x \le 3. | x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |…
  8. 8The variables x and y are connected by the equation y=x35−2x+2y=\frac{x^3}{5}-2x+2. Some corresponding values of x and y are giv…
  9. 9在y=3xy=3^{x}，y=log⁡0.3xy=\log _{0.3}x，y=x3y=x^{3}，y=xy= \sqrt {x}，这四个函数中当0<x1<x2<10 < x_{1} < x_{2} < 1时，使f(x1+x22)<f(x1)+f(x2)2f( \dfrac {x_{1}+x_{2}}{2}) < \dfrac {f(x_{1})+f(x_{2})}{2}…
  10. 10y=x34−2x+3y = \dfrac{x^3}{4} - 2x + 3. Complete the table of values for y=x34−2x+3y = \dfrac{x^3}{4} - 2x + 3. On the grid opposite, dra…
  11. 11The table below is for the function y=x34−2x+1y = \dfrac{x^{3}}{4} - 2x + 1. Complete the table of values for y=x34−2x+1y = \dfrac{x^{3}}{4} - 2x + 1…
  12. 12The curve y=a+bsin⁡cxy = a + b\sin cx is defined for 0≤x≤2π0 \le x \le 2\pi. The curve has a period of π\pi, and the minimum value o…
  13. 13Complete the table of values for y=2x2−2x.Valuesaregiventoonedecimalplacewhereappropriate.Onthegridopposite,drawthegraphofy=\dfrac{2}{x^{2}}-2x. Values are given to one decimal place where appropriate. On the grid opposite, draw the graph of …
  14. 14Answer the whole of this question on a piece of graph paper. The variables x and y are related by the equation y=x3−3x2+1y = x^3 - 3x^2 + 1…
  15. 15The table of values for y=x+5x−7y = x + \dfrac{5}{x} - 7 is given below. | x | 0.5 | 1 | 1.5 | 2 | 3 | 4 | 5 | 6 | 7 | |---|--…
  16. 16已知幂函数f(x)=(−m2+2m+4)xmf(x)=(-m^{2}+2m+4)x^{m}在(0,+∞)(0,+∞)上单调递减，则实数m=m=___.
  17. 17u is inversely proportional to the square of t. Sketch the graph of u=2t2u = \dfrac{2}{t^2}. Answer: Find the percentage ch…
  18. 18幂函数f(x)=xα(α∈R)f(x)=x^{α}(α∈R)过点(2,2)(2, \sqrt {2})，则f(16)=f(16)= ___ ．
  19. 19The variables x and y are connected by the equation y=13x(11−x2).Somecorrespondingvaluesofxandy,correctto1decimalplaces,aregiveninthefollowingtable.Calculatethevalueofp.Answerp=...Onthegridopposite,drawthegraphofy = \frac{1}{3}x(11 - x^2). Some corresponding values of x and y, correct to 1 decimal places, are given in the following table. Calculate the value of p. Answer p = ... On the grid opposite, draw the graph of …
  20. 20Let y=2x3−x2−10xy = 2x^3 - x^2 - 10x. Complete the table of values for y=2x3−x2−10xy = 2x^3 - x^2 - 10x. On the grid opposite, draw the grap…
  21. 21幂函数f(x)=x3m−11(m∈N)f(x)=x^{3m-11}(m\in N)在(0,+∞)(0,+\infty)上是减函数，且f(−x)=f(x)f(-x)=f(x)，则mm可能等于()(\quad) A. 00 B. 11 C. 22 D. 33…
  22. 22Sketch the graph of y=2x2y=\frac{2}{x^2} on the axes below. The point (1, 1) is shown in the diagram. Answer ... Sketch the…
  23. 23The variables x and y are connected by the equation y=32x+5x−7y = \frac{3}{2}x + \frac{5}{x} - 7. Some corresponding values of x…
  24. 24当n<0n < 0时，幂函数y=xny=x^{n}是定义域上的减函数.().() A. √√ B. ××
  25. 25If x is increased by 25%, find the percentage change in y. y = kx2\dfrac{k}{x^2} where k is a constant. Answer ... % Give…
  26. 26已知a>b>0a>b>0，则()(\quad) A. ln⁡1a<ln⁡1b\ln\dfrac{1}{a}< \ln \dfrac{1}{b} B. (1π)a>(1π)b(\dfrac{1}{π}{)}^{a}>(\dfrac{1}{\pi})^{b} C. a3<b3a^{3}< b^{3}…
  27. 27In the following graph, write down a possible value of n and the corresponding value of b for the equation. n = ... b =…
  28. 28Complete the table of values for y=10−x22−4xy = 10 - \frac{x^2}{2} - \frac{4}{x}. Complete the table of values for y=10−x22−4xy = 10 - \frac{x^2}{2} - \frac{4}{x}…
  29. 29Complete the table of values for y=2x+9x−11y = 2x + \dfrac{9}{x} - 11. Values are given to 1 decimal place where appropriate. |…
  30. 30已知函数f(x)=x12f(x)=x^{ \frac{1}{2}} ，则()() A. ∃x0∈R∃x_{0}∈R，f(x0)<0f(x_{0}) < 0 B. ∀x∈(0,+∞)∀x∈(0,+∞)，f(x)>0f(x) > 0 C. ∃x1∃x_{1}，x2∈[0,+∞)x_{2}∈[0,+∞)…
  31. 31Answer (b), (c) and (d) Complete the table of values for y = x35−x2+2\dfrac{x^3}{5} - x^2 + 2 . On the grid in the next page,…
  32. 32下列共有四个命题． (1)命题“∃x0∈R\exists {{x}_{0}}\in R，x02+1>3x0x_{0}^{2}+1 > 3{{x}_{0}}”的否定是“∀x∈R\forall x\in R，x2+1<3x{{x}^{2}}+1 < 3x”； (…
  33. 33The diagrams A, B, C, D, E and F show six graphs of different functions. yy is inversely proportional to xx, Diagram .…
  34. 34已知幂函数f(x)=(m−1)2xm2−4m+2f(x){=}{(m{-}1)}^{2}x^{m^{2}{-}4m{+}2}在(0,+∞)(0{,}{+∞})上单调递增，函数g(x)=2x−tg(x){=}2^{x}{-}t，对于任意的x1∈[1,6)x_{1}{∈[}1{,}6)，总存在x2∈[1,6)x_{2}{∈[}1{,}6)…
  35. 35The point (12,12)\left(\frac{1}{2},\frac{1}{2}\right) is shown on the axes. Sketch the graph of y=2x3y = 2x^3.
  36. 36The variables x and y are connected by the equation y=x32−5x−2y = \frac{x^3}{2} - 5x - 2. Some corresponding values of x and y a…
  37. 37Complete the table of values for y=2x+1x2−4y = 2x + \dfrac{1}{x^{2}} - 4. Values are given to two decimal places where appropria…
  38. 38From the diagrams above, select one of them which best illustrates each of the following statements. y=4πx3y = 4\pi x^3. The…