7) label the graphs with the correct functions. dotted: solid: a. $f(x)…

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

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

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).
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 $g(x) = -3 \cdot 3^x$: $g(-1) = -3 \cdot 3^{-1} = -1$

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

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

Click to enlarge

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 2026-02-09T19:57:22

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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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