Question

key features of graphs
6.
name:
even degree or odd degree?
end behavior:
x-intercepts:
y-intercept:
increasing interval:
decreasing interval:
relative minimum:
relative maximum:

Explanation:

1. Even Degree or Odd Degree?: The graph's ends both point downward (as \(x\to\infty\), \(f(x)\to-\infty\); as \(x\to-\infty\), \(f(x)\to-\infty\)), which matches the end behavior of an even-degree polynomial with a negative leading coefficient.
2. End Behavior: Describes the direction of the graph as \(x\) approaches positive and negative infinity.
3. X-Intercepts: Points where the graph crosses the x-axis (\(y=0\)), given on the graph.
4. Y-Intercept: Point where the graph crosses the y-axis (\(x=0\)), given on the graph.
5. Increasing Interval: The range of \(x\)-values where the graph rises from left to right, from the left x-intercept to the relative maximum.
6. Decreasing Interval: The range of \(x\)-values where the graph falls from left to right, from the relative maximum to the right x-intercept.
7. Relative Minimum: No point on the graph is lower than nearby points (the graph has no "valley" only a "peak").
8. Relative Maximum: The highest point on the graph, given as a coordinate pair.

Answer:

Even Degree or Odd Degree? Even Degree
End Behavior: As \(x\to\infty\), \(f(x)\to-\infty\); As \(x\to-\infty\), \(f(x)\to-\infty\)
X-Intercepts: \((-6.861, 0)\), \((5.238, 0)\)
Y-Intercept: \((0, 3)\)
Increasing Interval: \((-6.861, 1.6)\)
Decreasing Interval: \((1.6, 5.238)\)
Relative Minimum: None
Relative Maximum: \((1.6, 8.078)\)