基础代数：函数的基本概念- 取整函数
函数图像
常见的几种图像变换：
Suppose defines any function:
1. translates k units vertically (up if k>0; down if k<0);
2. translates h units horizontally (right if h>0; left if h<0);
3. stretches (shrinks) f(x) vertically by a factor of |a| if |a|>1 (|a|<1);
4. stretches (shrinks) f(x) horizontally by a factor of if |a|>1 (|a|<1);
5. reflects about the x-axis. (the reflection is vertical.);
6. reflects about the y-axis. (the reflection is horizontal.);
例题10. The function f(x) is graphed above. If g(x) = f(x) – 1,which of the following statements is TRUE?
(A) g(x) is greater than or equal to zero.
(B) g(x) is greater than or equal to negative one.
(C) g(x) is greater than or equal to negative two.
(D) g(x) is greater than negative one, but smaller than five.
Solution:
g(x) = f(x) – 1，图像整体向下平移一个单位，选C。
例题11. Which of the following equations represents the function f(x) = 2x – 1 shifted 2 units to the left on the my-plane?
(A) g(x) = 2x – 5
(B) g (x)– 3 = 2x
(C) g(x) = 2x + 1
(D) g(x)= 2x – 3
Solution：
向左移动，g(x)=f(x+2)=2(x+2)-1=2x+3
答案：B
例题12. A system of three equations and their graphs are shown here. How many solutions does the system of equations have?
(A) none
(B) one
(C) two
(D) three
Solution：
方程的解即为方程图像的交点，由图中可以看出，圆，直线，抛物线，三者交于一点，所以以上的方程组只有一解。
答案：B
例题13. The following figure shows the graph of f(x) from x = -6 to x = 6. If f(3) = a, what is f(a) ?
(A) -6
(B) -5
(C) 0
(D) 2
Solution：
f(3)=a=-5, f(-5)=2
答案：D。
例题14. The graph above shows the amount that a new, high-tech video arcade charges its customers.
What could the y-intercept of this graph represent?
A) The cost of playing 5 games
B) The cost per game, which is $5
C) The entrance fee to enter the arcade
D) The number of games that are played
Solution：
函数图像的理解：和Y轴的交点时，X值为零，所以这里的含义应该是基础费用。选C。
例题15. The graph of g(x) is shown in the figure above. If h(x) = -g(x) + 1, which of the following statements is true?
A) The range of h(x) is -3 ≤ y ≤ 3.
B) The minimum value of h(x) is -4.
C) The coordinates of point A on the function h(x) are (2, 4).
D) The graph of h(x) is increasing between x = -5 and x = -2.
Solution：
h(x) = -g(x) + 1 所对应的函数图像操作为：先关于X轴做对称，再向上平移一个单位。
原函数的值域为 [-2,4]，变化之后为[-3，3]，A正确。
答案：A。
