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・平移与特征挑战
The function p is defined by \( p(x)= a((x+5)^{2}−b) \) \( ((x+5)^{2}−c) \) , where a, b, and c are constants. In the xy-plane, the graph of \( y=p\left(x\right) \)passes through the points (\( -6,\ 24 \)) and (\( 0,\ 360 \)). What is the value of \( p(−10)+p(−4)? \)
原库参考解析
函数图象・平移与特征挑战
The graph of \( y=f\left(x\right)+4 \) is shown. Which equation defines the function \( f \) ?
原库参考解析
函数图象・平移与特征挑战
\( f\left(x\right)=4\left(x-a\right)\left(x-b\right)\left(x-c\right) \)
The function \( f \) is defined by the given equation, where a, b, and c are distinct constants. When\( a<x<b \), the value of \( f\left(x\right) \) is positive. The graph of \( y=f\left(x\right) \) in the xy-plane contains the point \( \left(r,\ s\right) \), where r and s are constants. If \( s=3 \), which of the following could be true?
Ⅰ.\( r<a \)
Ⅱ.\( b<r<c \)
Ⅲ.\( r>c \)
原库参考解析
函数图象・平移与特征挑战
The graph of \( y=f\left(x\right)+4 \) is shown. Which equation defines function \( f \) ？
原库参考解析
函数图象・平移与特征挑战
The graph of \( y=f\left(x\right)+2 \) is shown. Which equation defines function \( f \) ?
原库参考解析
函数图象・平移与特征挑战
The graph of \( y=f\left(x\right)+2 \) is shown. Which equation defines function \( f \) ?
原库参考解析
函数图象・平移与特征挑战
The graph of \( y=f\left(x\right)+2 \) is shown. Which equation defines function \( f \) ?
原库参考解析
函数图象・平移与特征挑战
The function f is defined by \( f\left(x\right)=-29^x \). The function g is a decreasing linear function. In the xy-plane, the graphs of \( y=f\left(x\right) \) and \( y=g\left(x\right) \) intersect at two points, (h, j) and (k, m), where j＞m. When \( g(x)<f(x) \), which of the following must also be true?
原库参考解析
函数图象・平移与特征挑战
The function \( f \) is defined by \( f(x)=-39^x \). The function g is a decreasing linear function. In the xy-plane, the graphs of \( y=f(x) \) and \( y=g(x) \) intersect at two points, \( (h,\ j) \) and\( (k,\ m) \), where \( j>m \). When \( g(x)<f(x) \), which of the following must also be true?
原库参考解析
函数图象・平移与特征进阶
\( f(x)=\frac{a-18}{x}+6 \)
In the given function \( f \), a is a constant. The graph of function \( f \) in the xy-plane, where \( y=f(x) \), is translated 3 units down and 9 units to the right to produce the graph of \( y=g(x) \). Which equation defines function g?
原库参考解析
函数图象・平移与特征挑战
The function g is defined by \( g\left(x\right)=-\frac{x}{4}+11 \). 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 the polynomial function \( f \) is shown, where \( y=f(x) \). What is the value of \( f(5) \)?
原库参考解析
