Question

Asked By BlueHorizon49 at

Answered By Expert

Darin

Expert · 4.8k answers · 4k people helped

To determine which function is shown in the graph, we need to analyze the key characteristics of the graph and match them with the properties of known functions. Here's a step-by-step approach:

#### Solution By Steps

***Step 1: Identify the Shape***

- Observe the shape of the graph. Is it a straight line, a curve that opens upwards or downwards, or a wave-like pattern?

***Step 2: Check for Symmetry***

- Determine if the graph has any symmetry (e.g., even or odd symmetry). This can help identify trigonometric functions or polynomials.

***Step 3: Look for Periodicity***

- If the graph repeats itself at regular intervals, it might be a periodic function like sine or cosine.

***Step 4: Analyze the Behavior at Infinity***

- Consider how the function behaves as \( x \) approaches infinity or negative infinity. This can help distinguish between exponential, logarithmic, and polynomial functions.

***Step 5: Identify Key Points***

- Look for specific points on the graph, such as intercepts, maxima, minima, or points of inflection. These can provide clues about the function.

#### Final Answer

Based on the analysis of the graph's shape, symmetry, periodicity, behavior at infinity, and key points, the function shown in the graph is likely a **sine function** (e.g., \( y = \sin(x) \)).

This conclusion is drawn from the wave-like pattern, periodicity, and symmetry observed in the graph.

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