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题目

解题步骤

1. Understand the question
   1. label the graphs with the correct functions.

   dashed:
   solid:
   a. $f(x)=e^{2x}$
   b. $g(x)=e^{3x}$

2. Explanation

   Step1: Analyze exponential growth behavior

   For exponential functions of the form $y = e^{kx}$, when $k>0$, the function increases as $x$ increases, and a larger $k$ means faster growth. When $x$ is negative, $y = e^{kx} = \frac{1}{e^{|kx|}}$, so a larger $k$ leads to a smaller $y$-value for negative $x$.

   Step2: Match graphs to functions

   The dashed graph decreases faster (has lower values) for negative $x$, so it corresponds to the function with the larger exponent coefficient, which is $g(x)=e^{3x}$. The solid graph decreases slower, so it corresponds to $f(x)=e^{2x}$.

3. Final answer

   dashed: $\boldsymbol{g(x)=e^{3x}}$
   solid: $\boldsymbol{f(x)=e^{2x}}$

答案

Question Analysis

OCR Text

4) label the graphs with the correct functions.
dashed:
solid:
a. $f(x)=e^{2x}$
b. $g(x)=e^{3x}$

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