Questions: Problem 5: (5 points each) Given two functions, f(x)=2^(x+1), g(x)=2^(-x+2) (1) Graph both functions f(x) and g(x) on the same given Cartesian plane.

Problem 5: (5 points each) Given two functions, f(x)=2^(x+1), g(x)=2^(-x+2) (1) Graph both functions f(x) and g(x) on the same given Cartesian plane.
Transcript text: Problem 5: (5 points each) Given two functions, $f(x)=2^{x+1}, g(x)=2^{-x+2}$ (1) Graph both functions $f(x)$ and $g(x)$ on the same given Cartesian plane.
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Solution

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Solution Steps

Step 1: Identify the Functions

The given functions are:

  • \( f(x) = 2^{x+1} \)
  • \( g(x) = 2^{-x+2} \)
Step 2: Simplify the Functions

Simplify the expressions for easier plotting:

  • \( f(x) = 2^{x+1} = 2 \cdot 2^x \)
  • \( g(x) = 2^{-x+2} = 2^2 \cdot 2^{-x} = 4 \cdot 2^{-x} \)

Final Answer

The functions to be plotted are:

  • \( f(x) = 2 \cdot 2^x \)
  • \( g(x) = 4 \cdot 2^{-x} \)

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -2, "ymax": 10}, "commands": ["y = 2_2**x", "y = 4_2**(-x)"], "latex_expressions": ["$f(x) = 2^{x+1}$", "$g(x) = 2^{-x+2}$"]}

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