Question: x intercept: $(2,4)$ yintercept: $(0,1)$ Positive: $x > 1$ Negative: $x < 1$ 4. x intercept: $(-2,0)$ y intercept: $(0,2)$ Positive: $-2 < x < 4$ Negative: $x < -2$ 5. x intercept: $(1,0)$ y intercept: $(0,3)$ Positive: $x > 1.5$ Negative: $x < 1.5$ 6. x intercept: y intercept: Positive: Negative: Graph 4: a piecewise linear graph with two line segments forms a peak in the center-top area; the left segment rises from the bottom-left toward the point near $(1,4)$, then the right segment falls toward the right side, position_hint = center. Graph 5: a straight line with negative slope descends from upper-left to lower-right, crossing the y-axis above the origin and the x-axis at about $(1,0)$, position_hint = center. Graph 6: a downward-opening parabola is centered slightly left of the y-axis, with a maximum near the top and both arms extending downward, position_hint = right.

1. **Problem Statement:** We are given information about the intercepts and sign behavior of three graphs (4, 5, and 6). We want to analyze and understand these graphs based on the given data. --- 2. **Graph 4 Analysis:** - $x$-intercept: $(-2,0)$ means the graph crosses the $x$-axis at $x = -2$. - $y$-intercept: $(0,2)$ means the graph crosses the $y$-axis at $y = 2$. - Positive region: $-2 < x < 4$ means the graph is above the $x$-axis between $x = -2$ and $x = 4$. - Negative region: $x < -2$ means the graph is below the $x$-axis for $x$ less than $-2$. Since the graph is piecewise linear with two line segments forming a peak near $(1,4)$, the left segment rises from bottom-left to near $(1,4)$ and the right segment falls toward the right side. --- 3. **Graph 5 Analysis:** - $x$-intercept: $(1,0)$ means the graph crosses the $x$-axis at $x = 1$. - $y$-intercept: $(0,3)$ means the graph crosses the $y$-axis at $y = 3$. - Positive region: $x > 1.5$ means the graph is above the $x$-axis for $x$ greater than $1.5$. - Negative region: $x < 1.5$ means the graph is below the $x$-axis for $x$ less than $1.5$. The graph is a straight line with negative slope descending from upper-left to lower-right. --- 4. **Graph 6 Analysis:** - No intercepts given. - The graph is a downward-opening parabola centered slightly left of the $y$-axis with a maximum near the top. - Both arms extend downward. --- 5. **Summary:** - Graph 4 is piecewise linear with a peak. - Graph 5 is a linear function with negative slope. - Graph 6 is a downward-opening parabola. --- 6. **Additional Notes:** - For Graph 4, the piecewise linear function can be described by two linear equations meeting at the peak. - For Graph 5, the line equation can be found using intercepts: slope $m = \frac{0 - 3}{1 - 0} = -3$, so equation is $y = -3x + 3$. - For Graph 6, without intercepts, the parabola can be modeled as $y = a(x - h)^2 + k$ with $a < 0$ and vertex near $(h,k)$ slightly left of $y$-axis. --- **Final answers:** - Graph 4: Piecewise linear with intercepts $(-2,0)$ and $(0,2)$, positive between $-2$ and $4$, negative left of $-2$. - Graph 5: Line $y = -3x + 3$ with intercepts $(1,0)$ and $(0,3)$, positive for $x > 1.5$, negative for $x < 1.5$. - Graph 6: Downward parabola centered slightly left of $y$-axis, no intercepts given.