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題目

解題步驟

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

   dashed:
   dotted:
   solid:
   a. $f(x)=e^x$
   b. $g(x)=3^x$
   c. $h(x)=2^x$

2. Brief Explanations

   For exponential functions \(a^x\) where \(a>1\), larger bases lead to faster growth as \(x\) increases, and faster decay as \(x\) decreases. At \(x=0\), all functions equal 1, matching the intersection point.

   1. The dashed graph is the middle-growing curve. Since \(2 < e \approx 2.718 < 3\), this matches \(f(x)=e^x\).
   2. The dotted graph grows slower than the dashed one, matching the smallest base: \(h(x)=2^x\).
   3. The solid graph grows the fastest, matching the largest base: \(g(x)=3^x\).
3. Final answer

   dashed: a. \(f(x) = e^x\)
   dotted: c. \(h(x) = 2^x\)
   solid: b. \(g(x) = 3^x\)

答案

Question Analysis

OCR Text

8) label the graphs with the correct functions.
dashed:
dotted:
solid:
a. $f(x)=e^x$
b. $g(x)=3^x$
c. $h(x)=2^x$

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