Horizontal Line 1Ec586

1. **Problem Statement:** Estimate the intercepts and identify the intervals where the function is positive and negative based on the graph. 2. **Given Information:** The graph is a horizontal line along $$y = 4$$. 3. **Finding the x-intercept:** The x-intercept occurs where $$y = 0$$. Since the line is at $$y = 4$$ and never touches $$y = 0$$, there is **no x-intercept**. 4. **Finding the y-intercept:** The y-intercept occurs where $$x = 0$$. At $$x = 0$$, $$y = 4$$, so the y-intercept is $$(0, 4)$$. 5. **Determining intervals where the function is positive or negative:** Since $$y = 4$$ for all $$x$$, and $$4 > 0$$, the function is **positive for all real numbers**. The function is **never negative**. **Final answers:** - x-intercept: none - y-intercept: $$(0, 4)$$ - Positive interval: $$(-\infty, \infty)$$ (all real numbers) - Negative interval: none