nakresli 2 grafy k charakteristikám exponenciálních funkcí: **Charakteristika:**

Pokud je a>1*a*>1 (např. 2x2*x*), funkce roste. To znamená, že jakmile zvýšíme x*x*, hodnota f(x)*f*(*x*) se zvyšuje.

Pokud je 0<a<10<*a*<1 (např. (1/2)x(1/2)*x*), funkce klesá. To znamená, že jakmile zvýšíme x*x*, hodnota f(x)*f*(*x*) se snižuje.

Here are the two graphs illustrating the characteristics of exponential functions:

1. **Growing Exponential Function (a > 1)**: This graph shows a function like \(f(x) = 2^x\), which rises sharply as \(x\) increases.
   
2. **Decaying Exponential Function (0 < a < 1)**: This graph shows a function like \(f(x) = (1/2)^x\), which decreases and approaches zero as \(x\) increases.

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### Related Questions:
1. What are the key properties of exponential functions?
2. How do the base values of exponential functions affect their graphs?
3. What is the relationship between exponential growth and logarithmic functions?
4. How can exponential functions model real-world phenomena?
5. What are some applications of exponential decay in science and engineering?

**Tip:** When working with exponential functions, remember that the base determines the growth or decay rate: a base greater than 1 leads to growth, while a base between 0 and 1 results in decay.

nakresli 2 grafy k charakteristikám exponenciálních funkcí: Charakteristika: Pokud je a>1 (např. 2^x), funkce roste. To znamená, že jakmile zvýšíme x, hodnota f(x) se zvyšuje. Pokud je 0<a<1 (např. (1/2)^x), funkce klesá. To znamená, že jakmile zvýšíme x, hodnota f(x) se snižuje.

Explore the characteristics of exponential functions with graphs showing growth (a > 1) and decay (0 < a < 1). Understand how the base of an exponential function affects its behavior as x increases, suitable for Grades 9-12.

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