Question

sketch the graph of the function below, including correct signs, ( x )-intercepts and ( y )-intercepts. f(x) = (x + 6)(x + 4)(x + 1)(x - 2)^2 plot the ( y )-intercept and the roots. click on the graph to plot a point. click a point again to delete it.

Explanation:

Step3: Note multiplicity behavior

For $x=2$ (multiplicity 2), the graph touches the x-axis and turns around. For roots with multiplicity 1 ($x=-6,-4,-1$), the graph crosses the x-axis.

Step4: End behavior

Degree of polynomial is $1+1+1+2=5$ (odd), leading coefficient positive. As $x\to\infty$, $f(x)\to\infty$; as $x\to-\infty$, $f(x)\to-\infty$.

Answer:

Step3: Note multiplicity behavior

For $x=2$ (multiplicity 2), the graph touches the x-axis and turns around. For roots with multiplicity 1 ($x=-6,-4,-1$), the graph crosses the x-axis.

Step4: End behavior

Degree of polynomial is $1+1+1+2=5$ (odd), leading coefficient positive. As $x\to\infty$, $f(x)\to\infty$; as $x\to-\infty$, $f(x)\to-\infty$.