To solve this question, let's analyze the given information.

The problem states:

• Equation: $y = \left( \frac{1}{2} \right)^x$
• Graph: The question asks if the given graph represents the equation $y = \left( \frac{1}{2} \right)^x$.

Step-by-Step Analysis:

1. Function Type:

   • The equation $y = \left( \frac{1}{2} \right)^x$ represents an exponential decay function because the base $\frac{1}{2}$ is between 0 and 1.
   • This type of function generally decreases as $x$ increases.

2. Expected Graph Shape:

   • For $y = \left( \frac{1}{2} \right)^x$:
     • As $x \to +\infty$, $y \to 0$ (the graph approaches the x-axis from above).
     • As $x \to -\infty$, $y \to +\infty$ (the graph rises sharply for negative $x$ values).

3. Graph Observation:

   • The graph shown in the image appears to be increasing as $x$ increases, which is characteristic of an exponential growth function, not exponential decay.
   • This suggests the graph might represent a function like $y = 2^x$, where the base is greater than 1, rather than $y = \left( \frac{1}{2} \right)^x$.

Conclusion:

The statement in the question is false. The graph does not represent the function $y = \left( \frac{1}{2} \right)^x$.

Would you like more details or have any further questions?

Here are 5 related questions:

1. What are the characteristics of exponential growth and decay functions?
2. How does the base of an exponential function affect its graph?
3. What are some real-world examples of exponential decay?
4. How can we determine the y-intercept of an exponential function?
5. How do transformations affect the graph of an exponential function?

Tip: For exponential functions, if the base is between 0 and 1, the function represents decay; if the base is greater than 1, it represents growth.