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 graph of \( y=f\left(x\right) \) is shown where \( f\left(x\right)=ax^3+bx^2+cx+d \) and a, b, c, and d are constants. For how many distinct values of x does \( f\left(x\right)=0 \) ?
原库参考解析
函数图象・平移与特征挑战
In the xy-plane, the graph of the equation \( y=6^x \) is translated 8 units down. What is an equation of the resulting graph?
原库参考解析
函数图象・平移与特征挑战
The function p is defined by \( p\left(x\right)=a\left(\left(x+6\right)^2-b\right)\left(\left(x+6\right)^2-c\right) \) , where a, b, and c are constants. In the xy-plane, the graph of \( y=p\left(x\right) \) passes through the points (\( −7 \), \( 24 \) )and (\( 0 \), \( 899 \)). What is the value of \( p(−12)+p(−5) \) ?
原库参考解析
函数图象・平移与特征挑战
The graph of the linear function y = f (x) + 13 is shown. If c and d are positive constants, which equation could define f?
原库参考解析
函数图象・平移与特征进阶
For line h, the table shows three values of x and their corresponding values of y. Line k is the result of translating line h down 4 units in the xy-plane. What is the x-intercept of line k?
原库参考解析
函数图象・平移与特征挑战
The function f is defined by \( f\left(x\right)=7x-135 \). If the point (k, 2k) lies on the graph of \( y=f\left(x\right) \) in the xy-plane, where k is a constant, what is the value of k?
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・平移与特征进阶
The graph of \( y=f\left(x\right)-k \) is shown in the xy-plane. If k, a, and b are positive constants, which equation could define \( f \) ?
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 \( y=f\left(x\right) \). What is the value of \( f\left(0\right) \)?
原库参考解析
函数图象・平移与特征进阶
The function \( f \) is defined by \( f\left(x\right)=3x^5 \). In the xy-plane, the graph of \( y=g\left(x\right) \) is the result of shifting the graph of \( y=f\left(x\right) \) up 9 units. Which equation defines the function g?
原库参考解析
函数图象・平移与特征进阶
The functions \( f \) and \( g \)are defined as \( f\left(x\right)=\frac{1}{5}x-9 \) and\( g\left(x\right)=\frac{4}{5}x+27 \). If the function \( h \) is defined as \( h\left(x\right)=f\left(x\right)+g\left(x\right) \), what is the x-intercept of the graph of \( y=h\left(x\right) \)in the xy-plane?
原库参考解析
函数图象・平移与特征进阶
In the xy-plane, the graph of the equation \( y=9^x \) is translated 8 units down. What is an equation of the resulting graph?
原库参考解析
