4) label the graphs with the correct functions. dashed: solid: a. $f(x)…
dashed: $\boldsymbol{g(x)=e^{3x}}$ solid: $\boldsymbol{f(x)=e^{2x}}$
Question
- label the graphs with the correct functions.
dashed:
solid:
a. $f(x)=e^{2x}$
b. $g(x)=e^{3x}$
Solution Steps
-
Understand the question
- label the graphs with the correct functions.
dashed:
solid:
a. $f(x)=e^{2x}$
b. $g(x)=e^{3x}$ -
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 $f(x)=e^{2x}$.
-
Final answer
dashed: $\boldsymbol{g(x)=e^{3x}}$
solid: $\boldsymbol{f(x)=e^{2x}}$
Answer
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 $f(x)=e^{2x}$.
Answer
dashed: $\boldsymbol{g(x)=e^{3x}}$
solid: $\boldsymbol{f(x)=e^{2x}}$
Question Image
Click to enlargeQuestion Analysis
Subject
mathematics
Sub Subject
calculus
Education Level
high school
Difficulty
unspecified
Question Type
with chart, multiple choice
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-02-09T19:51:29
OCR Text
Show OCR extraction
4) label the graphs with the correct functions.
dashed:
solid:
a. $f(x)=e^{2x}$
b. $g(x)=e^{3x}$
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