To determine which of the given graphs corresponds to the inequality [tex]\( x^2 \leq 4 \)[/tex], let's go through a detailed, step-by-step solution.
### Step-by-Step Solution:
1. Understand the Inequality:
- The inequality [tex]\( x^2 \leq 4 \)[/tex] involves a quadratic expression.
- We need to understand the range of [tex]\( x \)[/tex] that satisfies this inequality.
2. Rewrite the Inequality:
- Starting from the inequality [tex]\( x^2 \leq 4 \)[/tex], we can solve for [tex]\( x \)[/tex].
3. Solve for [tex]\( x \)[/tex]:
- To isolate [tex]\( x \)[/tex], we take the square root of both sides, noting that this gives us two solutions:
[tex]\[
x^2 \leq 4
\][/tex]
[tex]\[
-\sqrt{4} \leq x \leq \sqrt{4}
\][/tex]
[tex]\[
-2 \leq x \leq 2
\][/tex]
- This tells us that [tex]\( x \)[/tex] must lie within the interval [tex]\([-2, 2]\)[/tex].
4. Interpret the Solution:
- The solution to the inequality includes all values of [tex]\( x \)[/tex] between [tex]\(-2\)[/tex] and [tex]\(2\)[/tex] inclusive.
- A graph of this inequality would show a horizontal number line shaded from [tex]\(-2\)[/tex] to [tex]\(2\)[/tex], including these endpoints.
5. Evaluate the Graph Options:
- You are provided with several graph options: A, B, C, D, E, and F.
- The correct graph should show the interval [tex]\([-2, 2]\)[/tex] as the shaded or represented region.
Given the solution and understanding of the problem, the correct graph option is Graph B, which properly represents the range of [tex]\( x \)[/tex] between [tex]\(-2\)[/tex] and [tex]\(2\)[/tex] inclusive.
Thus, the answer to the question is:
B. Graph B
