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
\( f\left(x\right)=3d\left(26x+27\right)+18 \)
Which of the following represents the x-intercept of the graph of \( y=f(x)+6 \) in the xy-plane, where d is a constant?
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 \( f(2) \) ?
原库参考解析
函数图象・平移与特征挑战
The function \( f \) is defined by \( f(x)=24x^3 \) . The graph of \( y=f(-x)+c \) in the xy-plane, where c is a positive integer constant, has an x-intercept at (r, 0) and a y-intercept at (0, t), where r and t are constants. Which of the following must be true about r and t?
原库参考解析
函数图象・平移与特征进阶
What is an equation of the graph shown?
原库参考解析
函数图象・平移与特征挑战
\( r(x)=\frac{p}{x-4}+16 \)
The given equation defines the function r , where p is a positive constant. The graph of \( y=r(x) \) in the xy-plane is translated 7 units to the left to produce the graph of \( y=t(x) \). Which equation defines function t ?
原库参考解析
函数图象・平移与特征进阶
The complete graph of \( y=f(x) \) is shown. For how many values of \( x \) does \( f(x)=0 \)?
原库参考解析
函数图象・平移与特征挑战
\( g(x)=2(14x-15) \)
What is the y-coordinate of the y-intercept of the graph of \( y=g(x)-5 \) in the xy-plane?
原库参考解析
函数图象・平移与特征挑战
The graph of the function C shows the estimated number of chirps a field cricket makes per minute as a function of the temperature x, in degrees Fahrenheit \( (^{∘}\text{F}) \) , where \( y=C(x) \). According to the graph, what is the estimated number of chirps, to the nearest whole number, a field cricket makes per minute when the temperature is \( 44^{∘}\text{F} \) ?
原库参考解析
函数图象・平移与特征进阶
The function \( f \) is defined by \( f(x)=(x-2)(x-8)(x+3) \). In the xy-plane, the graph of \( y=h(x) \) is the result of translating the graph of \( y=f(x) \) up 6 units. What is the y-coordinate of the y-intercept of the graph of \( y=h(x) \)?
原库参考解析
函数图象・平移与特征进阶
The graph of \( y=\left(\frac{1}{4}\right)^x+1 \) in the xy-plane is shifted up 5 units. What is an equation of the resulting graph?
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 \( y=5^x \) is translated 3 units down. What is an equation of the resulting graph?
参考答案
函数图象・平移与特征挑战
The complete graph of \( y=f(x) \) is shown. For how many values of x does \( f(x)=0 \)?
参考答案
