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問題

解法ステップ

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

   dotted:
   solid:
   a. $f(x) = -2 \\cdot 3^{x}$
   b. $g(x) = -3 \\cdot 3^{x}$

2. Brief Explanations
   1. For exponential functions of the form $y = k \cdot 3^x$, when $k$ is negative, the function is reflected over the x-axis. The magnitude of $k$ determines how "steep" the curve is: a larger magnitude means the function decreases faster as $x$ increases (moves right) and becomes more negative faster as $x$ decreases (moves left).
   2. Test $x=-1$ for both functions:

   • For $f(x) = -2 \cdot 3^x$: $f(-1) = -2 \cdot 3^{-1} = -\frac{2}{3} \approx -0.67$
   • For $g(x) = -3 \cdot 3^x$: $g(-1) = -3 \cdot 3^{-1} = -1$

   1. The dotted graph passes through $x=-1, y\approx-0.67$, matching $f(x)$. The solid graph passes through $x=-1, y=-1$, matching $g(x)$.
3. Final answer

   dotted: a. $f(x) = -2 \cdot 3^x$
   solid: b. $g(x) = -3 \cdot 3^x$

答え

Question Analysis

OCR Text

7) label the graphs with the correct functions.
dotted:
solid:
a. $f(x) = -2 \\cdot 3^{x}$
b. $g(x) = -3 \\cdot 3^{x}$

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