Questions: The function f graphed below is defined by a polynomial expression of degree 4. Use the graph to solve the exercise. The solutions of the equation f(x)=0 are the x-intercepts of the graph of f. The solution of the inequality f(x) ≥ 0 is the set of x-values at which the graph of f is on or above the x-axis. From the graph of f we find that the solutions of the equation f(x)=0 are x= (Enter your answers as a comma-separated list.) The solution of the inequality f(x) ≥ 0 is (Enter your answer using interval notation.)

The function f graphed below is defined by a polynomial expression of degree 4. Use the graph to solve the exercise. The solutions of the equation f(x)=0 are the x-intercepts of the graph of f. The solution of the inequality f(x) ≥ 0 is the set of x-values at which the graph of f is on or above the x-axis. From the graph of f we find that the solutions of the equation f(x)=0 are x= (Enter your answers as a comma-separated list.) The solution of the inequality f(x) ≥ 0 is (Enter your answer using interval notation.)
Transcript text: The function $f$ graphed below is defined by a polynomial expression of degree 4. Use the graph to solve the exercise. The solutions of the equation $f(x)=0$ are the $x$-intercepts of the graph of $f$. The solution of the inequality $f(x) \geq 0$ is the set of $x$-values at which the graph of $f$ is on or above the $x$-axis. From the graph of $f$ we find that the solutions of the equation $f(x)=0$ are $x=$ $\square$ (Enter your answers as a comma-separated list.) The solution of the inequality $f(x) \geq 0$ is $\square$ (Enter your answer using interval notation.)
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Solution

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Solution Steps

Step 1: Identify the x-intercepts

The x-intercepts of the graph are the points where the function \( f(x) = 0 \). From the graph, these points are where the curve crosses the x-axis.

Step 2: Determine the x-intercepts

From the graph, the x-intercepts are approximately at \( x = 0.5 \), \( x = 2 \), and \( x = 3.5 \).

Step 3: Solve the inequality \( f(x) \geq 0 \)

The inequality \( f(x) \geq 0 \) represents the x-values where the graph is on or above the x-axis. From the graph, these intervals are:

  • From \( x = 0 \) to \( x = 0.5 \)
  • From \( x = 2 \) to \( x = 3.5 \)

Final Answer

  • The solutions of the equation \( f(x) = 0 \) are \( x = 0.5, 2, 3.5 \).
  • The solution of the inequality \( f(x) \geq 0 \) is \( [0, 0.5] \cup [2, 3.5] \).
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