Math Problem Statement

La función f está definida por la regla f(x) = 2^x. Hallar f(x) para cada valor de x en la tabla.

Solution

The problem defines the function f(x)=2xf(x) = 2^x and asks to find f(x)f(x) for each given value of xx in the table.

Let's calculate f(x)f(x) for each value of xx in the table:

  1. When x=−3x = -3: f(−3)=2−3=123=18=0.125f(-3) = 2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125

  2. When x=−2x = -2: f(−2)=2−2=122=14=0.25f(-2) = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} = 0.25

  3. When x=−1x = -1: f(−1)=2−1=12=0.5f(-1) = 2^{-1} = \frac{1}{2} = 0.5

  4. When x=0x = 0: f(0)=20=1f(0) = 2^0 = 1

  5. When x=1x = 1: f(1)=21=2f(1) = 2^1 = 2

The completed table should look like this:

\hline x & f(x) \\ \hline -3 & 0.125 \\ -2 & 0.25 \\ -1 & 0.5 \\ 0 & 1 \\ 1 & 2 \\ \hline \end{array}$$ Would you like further details or have any questions? Here are 5 related questions to consider: 1. How would the values change if $$f(x) = 3^x$$ instead? 2. What happens to $$f(x)$$ as $$x$$ approaches very large positive values? 3. What is the behavior of $$f(x)$$ as $$x$$ approaches very large negative values? 4. How does the function $$f(x) = 2^x$$ compare to $$g(x) = 10^x$$? 5. What would $$f(x)$$ be for non-integer values of $$x$$, such as $$x = 0.5$$? **Tip:** In exponential functions, as $$x$$ increases, $$f(x) = 2^x$$ grows very quickly, while it approaches zero as $$x$$ decreases.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Evaluating Functions

Formulas

f(x) = 2^x

Theorems

-

Suitable Grade Level

Grades 7-9

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