Question

6.5 graphing and solving exponential functions quiz

the graph of (f(x) = (1/3)^x) represents exponential growth.

true
false

Explanation:

Identify the function form

Using the Exponential Growth and Exponential Decay knowledge points

$$ f(x) = a \cdot b^x, \quad a = 1, \quad b = \frac{1}{3} $$

Analyze the base value

Using the Exponential Growth and Exponential Decay knowledge points

$$ 0 < b < 1 \implies 0 < \frac{1}{3} < 1 $$

Determine the behavior

Using the Exponential Decay knowledge point

$$ \text{Since } 0 < b < 1, \text{ the function represents exponential decay, not growth.} $$

Answer:

• True
• False (Correct answer)