Questions: 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 $f(x)=4$.

Solution

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.

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

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