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 \( g(x)=−\frac{x}{3}+11. \)What is the \( x \)-intercept of the graph of \( y=g(x)+5 \) in the \( xy \)-plane?
参考答案
函数图象・平移与特征进阶
\( f(x)=\frac{a-14}{x}+6 \)
In the given function \( f \), \( a \) is a constant. The graph of function \( f \) in the xy-plane, where \( y=f(x) \), is translated 2 units down and 7 units to the right to produce the graph of \( y=g(x) \). Which equation defines function g?
In the given function \( f \), \( a \) is a constant. The graph of function \( f \) in the xy-plane, where \( y=f(x) \), is translated 2 units down and 7 units to the right to produce the graph of \( y=g(x) \). Which equation defines function g?
参考答案
函数图象・平移与特征基础
The graph of the function \( f \) is shown, where \( y=f(x) \). What is the value of \( f(0) \)?
参考答案
函数图象・平移与特征进阶
The function \( f \) is defined by \( f\left(x\right)=\left(x-10\right)\left(x-8\right)\left(x-4\right) \). In the xy-plane, the graph of \( y=g\left(x\right) \) is the result of translating the graph of \( y=f\left(x\right) \) up 6 units. What is the value of \( g\left(0\right) \) ?
原库参考解析
函数图象・平移与特征进阶
The graph of the function \( f\left(x\right) \) is shown, where \( y=f\left(x\right) \) .What is the value of \( f\left(0\right) \) ?
原库参考解析
函数图象・平移与特征基础
The function \( f \) is defined by \( f\left(x\right)=7x^3 \) . In the xy-plane, the graph of \( y=g\left(x\right) \) is the result of shifting the graph of \( y=f\left(x\right) \) down 2 units. Which equation defines function g?
原库参考解析
函数图象・平移与特征进阶
The graph of the function \( f \) is shown, where\( y=f\left(x\right) \).
Which of the following best describes the function \( f \)?
原库参考解析
函数图象・平移与特征挑战
The graph of \( y=g(x) \) is shown. If \( g(x+28)=\frac{1}{10}(x-a)^2(x-b)^2(x-c) \) , where a, b, and c are constants, which of the following could be the value of b?
原库参考解析
函数图象・平移与特征挑战
The graph of y = f(x) + 14 is shown. Which equation defines function f?
原库参考解析
函数图象・平移与特征基础
The line graph shows the estimated number of chipmunks in a state park on April 1 of each year from 1989 to 1999.
Based on the line graph, in which year was the estimated number of chipmunks in the state park the greatest?
原库参考解析
函数图象・平移与特征基础
Function f is defined by f(x)= (x + 6)(x + 5)(x + 1). Function g is defined by g(x)= f(x - 1). The graph of y = g(x) in the xy-plane has x-intercepts at (a, 0), (b, 0), and (c, 0), where a, b, and c are distinct constants. What is the value of a + b + c?
原库参考解析
函数图象・平移与特征挑战
The function f is defined by f(x) = (x - 6)(x - 2)(x + 6). In the xy-plane, the graph of y = g(x) is the result of translating the graph of y = f(x) up 4 units. What is the value of g(0)?
原库参考解析
