Questions: The graph of f(x)=x^3-5x-2 is shown below. Estimate the solution(s) to the equation f(x)=4.

The graph of f(x)=x^3-5x-2 is shown below. Estimate the solution(s) to the equation f(x)=4.
Transcript text: The graph of $f(x)=x^{3}-5 x-2$ is shown below. Estimate the solution(s) to the equation $f(x)=4$.
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Solution

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Solution Steps

Step 1: Understand the Problem

We need to estimate the solutions to the equation \( f(x) = 4 \) using the given graph of \( f(x) = x^3 - 5x - 2 \).

Step 2: Identify the Line \( y = 4 \)

On the graph, locate the horizontal line where \( y = 4 \).

Step 3: Find the Intersection Points

Determine where the graph of \( f(x) \) intersects the line \( y = 4 \). These intersection points represent the solutions to the equation \( f(x) = 4 \).

Step 4: Estimate the x-Coordinates

From the graph, estimate the x-coordinates of the intersection points.

Final Answer

The solutions to the equation \( f(x) = 4 \) are approximately \( x \approx -2.5 \) and \( x \approx 2.5 \).

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