Question

slt12: key features of graphs
name:
4.
even degree or odd degree?
end behavior:
x-intercepts:
y-intercept:
increasing interval:
decreasing interval:
relative minimum:
relative maximum:
(marked points on the graph: (-1,1.25), (0,0), (-1.8541,0), (4.8541,0), (3,-6.75))

Explanation:

Step1: Identify degree from ends

The graph's left end goes down ($x\to-\infty, f(x)\to-\infty$) and right end goes up ($x\to+\infty, f(x)\to+\infty$), so it is odd degree.

Step2: State end behavior

As $x\to-\infty$, $f(x)\to-\infty$; as $x\to+\infty$, $f(x)\to+\infty$.

Step3: List x-intercepts

These are the points where the graph crosses the x-axis: $(-1.8541, 0)$, $(0, 0)$, $(4.8541, 0)$.

Step4: Find y-intercept

This is where the graph crosses the y-axis: $(0, 0)$.

Step5: Find increasing interval

The graph rises from $x=3$ to $+\infty$, so the interval is $(3, \infty)$.

Step6: Find decreasing interval

The graph falls from $-\infty$ to $x=3$, so the interval is $(-\infty, 3)$.

Step7: Identify relative minimum

This is the lowest point on the graph: $(3, -6.75)$.

Step8: Identify relative maximum

This is the highest point on the graph: $(-1, 1.25)$.

Answer:

Even Degree or Odd Degree? Odd Degree
End Behavior: As $x\to-\infty$, $f(x)\to-\infty$; as $x\to+\infty$, $f(x)\to+\infty$
X-Intercepts: $(-1.8541, 0)$, $(0, 0)$, $(4.8541, 0)$
Y-Intercept: $(0, 0)$
Increasing Interval: $(3, \infty)$
Decreasing Interval: $(-\infty, 3)$
Relative Minimum: $(3, -6.75)$
Relative Maximum: $(-1, 1.25)$