这部分需要会什么？
- 使用指数运算法则改写表达式
- 用同底数解指数方程
- 理解指数函数的初始值与每单位倍率
核心概念与公式
在表达式有定义的前提下，\(a^ma^n=a^{m+n}\)，\(a^m/a^n=a^{m-n}\)，\((a^m)^n=a^{mn}\)。除法和负指数要求底数非零；涉及任意实数指数时通常取正底数。
指数函数 \(y=Ab^x\)（\(A>0,b>0,b\ne1\)）的初始值为 \(A\)，输入每增加 1，输出乘 \(b\)。当 \(b>1\) 时递增；\(0<b<1\) 时递减。指数方程能改成相同正底数且底数不为 1 时，可以比较指数。
做题时怎样使用
- 先检查底数能否写成同一个数的幂
- 区分“幂相乘”与“指数相乘”，逐步简化
- 解释函数时，找出输入增加 1 对输出造成的倍率
容易混淆的地方
\(a^m+a^n\) 一般不能合并成 \(a^{m+n}\)。\(A\) 是乘在指数项外面的系数，不是底数。
用一个例题串起方法
知识点教学例题展开解题思路 ＋
统一底数为 2：\(2^{3x-3}=2^{2x+2}\)。由于底数为 2，可令指数相等，得 \(3x-3=2x+2\)，所以 \(x=5\)。
本知识点题库
先独立作答，再查看答案与解析。
The graph of \( y=f\left(x\right) \) is shown, where \( f\left(x\right)=ab^x+c \) , and a, b, and c are constants. For how many values of x does \( f\left(x\right)=0 \) ?
The function \( f \) is defined by \( f\left(x\right)=-10\left(3\right)^x+\frac{1}{k} \) , where k is a constant. If \( y=f\left(x\right) \) is graphed in the xy-plane, what is the y-coordinate of the y-intercept of the graph?
The function \( f \) is defined by \( f\left(x\right)=ab^{\frac{x}{n}} \) , where a, b and n are constants, and b and n are integers. If \( f\left(4\right)=5 \) and \( f\left(7\right)=135 \) . What is the value of \( f\left(9\right) \) ?
The graph of \( y=f\left(x\right) \) is shown, where \( f\left(x\right)=ab^x+c \) and a, b and c are constants. For how many values of x does \( f\left(x\right)=0 \) ?
The equation of the graph shown is \( y=a^x+b \) , where a and b are constants. What is the value of \( a−b \) ?
The functions \(f\) and \(g\) are defined by the equations shown, where \(a\) and \(b\) are integer constants, \(a<b\), and \(b<0\). If \(y=f(x)\) and \(y=g(x)\) are graphed in the \(xy\)-plane, which of the following equations displays, as a constant or coefficient, the \(y\)-coordinate of the \(y\)-intercept of the graph of the corresponding function?
I. \(f(x)=a(2.1)^{x+b}\)
II. \(g(x)=a(2.1)^x+b\)
For the exponential function g, the table shows four values of x and their corresponding values of \( g\left(x\right) \). Which equation defines g?
What is the y-intercept of the graph of \( y=14^x \) in the xy-plane?
\( f\left(x\right)=7\left(4\right)^x \)
The function \( f \) is defined by the given equation. If \( g(x)=f(x+3) \) , which of the following equations defines the function g?
What is the y-intercept of \( y=-(4)^x-39 \) in the xy-plane?
What is the y-intercept of the graph of \( y=\left(\frac{8}{13}\right)^{x+1} \) in the xy-plane?
What is the y-intercept of the graph of \( y=16^x \) in the xy-plane?
