这部分需要会什么？
- 从图象读取定义域、值域、截距和增减区间
- 解释水平与竖直平移
- 理解伸缩和反射如何改变图象上的点
核心概念与公式
\(y=f(x-h)+k\) 把原图象向右平移 \(h\)、向上平移 \(k\)；负值表示反方向。若原图象上有 \((a,b)\)，新图象上就有 \((a+h,b+k)\)。
\(y=Af(x)\) 将纵坐标乘 \(A\)，\(A<0\) 时还关于横轴反射；\(y=f(Bx)\)（\(B\ne0\)）将横坐标除以 \(B\)，\(B<0\) 时还关于纵轴反射。定义域看横坐标范围，值域看纵坐标范围；实心点包含端点，空心点不包含。
做题时怎样使用
- 先从图象找可靠的关键点，如顶点、端点和截距
- 水平变化看函数括号里面，竖直变化看外面
- 使用点的坐标变化验证方向，再读取需要的函数特征
容易混淆的地方
\(f(x+3)\) 是向左 3，不是向右 3。函数值为正和函数递增是不同概念：一个看位置，一个看变化趋势。
用一个例题串起方法
知识点教学例题\(f\) 的图象经过 \((2,5)\)。\(g(x)=f(x-3)-4\) 的图象必经过哪个对应点？
展开解题思路 ＋
新图象向右 3、向下 4，因此对应点为 \((2+3,5-4)=(5,1)\)。代入检验：\(g(5)=f(2)-4=1\)。
本知识点题库
先独立作答，再查看答案与解析。
函数图象・平移与特征进阶
The function g is defined by g(x) =\( \frac{1}{m}x \)+21 , where m is an integer constant and14≤ m ≤17. For the graph of y = g(x) -9 in the xy-plane, what is the x-coordinate of a possible x-intercept?
原库参考解析
函数图象・平移与特征进阶
The function g is defined by \( g\left(x\right)=-\frac{x}{3}+11 \). What is the x-intercept of the graph of y=g(x)+6 in the xy-plane?
原库参考解析
函数图象・平移与特征挑战
f(x) = (x - 2)(x ＋4)(x - 3)
In the xy-plane, when the graph of the function f, where y = f(x), is shifted up 6 units, the resulting graph is defined by the function g. If the graph of y= g(x) crosses through the point (5,b), where b is a constant, what is the value of b?
原库参考解析
函数图象・平移与特征进阶
The function g is defined by \( g\left(x\right)=-\frac{x}{5}+12 \) . What is the x-intercept of the graph of\( y=g\left(x\right)+7 \) in the xy-plane?
原库参考解析
函数图象・平移与特征进阶
The graph of y = f(x) -9 is shown.
Which equation defines the linear function f?
原库参考解析
函数图象・平移与特征挑战
f (x) = (x − 2)(x − 5)(x + 9)
The above function f (x) is the result of translating g (x) up 5 units. What is the y-intercept of g (x)?
原库参考解析
函数图象・平移与特征挑战
The graph shows the estimated concentration of a certain strain of bacteria, in millions of cells per mL of nutrient medium, over time x, in minutes since the initial measurement. According to the graph, which of the following is closest to the number of minutes in took for the estimated concentration of the bacteria to increase from 20 million cells per mL of nutrient medium to 30 million cells per mL of nutrient medium?
原库参考解析
函数图象・平移与特征挑战
g(x)=2(16x-17)What is the y-coordinate of the y-intercept of the graph of y=g(x)-3 in the xy-plane?
原库参考解析
函数图象・平移与特征挑战
The graph shows the estimated concentration of a certain strain of bacteria, y , in millions of cells per mL of nutrient medium, over time x, in minutes since the initial measurement. According to the graph, which of the following is closest to the number of minutes it took for the estimated concentration of the bacteria to increase from 20 million cells per mL of nutrient medium to 30 million cells per mL of nutrient medium?
原库参考解析
函数图象・平移与特征挑战
g(x) = 2(16x -17)
What is the y-coordinate of the y-intercept of the graph of y = g(x) - 3 in the xy-plane?
原库参考解析
函数图象・平移与特征挑战
p(x) = \( 9\left(2\right)^{\frac{x}{4}}+9 \)
What is the y-intercept of the graph of y = p(x) in the xy-plane?
原库参考解析
函数图象・平移与特征挑战
The graph of y = f (x)+ 3 is shown. Which equation defines function f ?
原库参考解析
