sketch the graph of the function below, including correct signs, x - intercepts and y - intercepts.\n\n$f(x)=…

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

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

Answer

Explanation:

Step1: Find x - intercepts

Set $f(x)=0$. Then $(x + 1)^2(x - 1)^2=0$. Using the zero - product property, if $ab = 0$, then $a = 0$ or $b = 0$. So $(x + 1)^2=0$ gives $x=-1$ and $(x - 1)^2=0$ gives $x = 1$. The x - intercepts are $x=-1$ and $x = 1$.

Step2: Find y - intercept

Set $x = 0$. Then $f(0)=(0 + 1)^2(0 - 1)^2=(1)^2(-1)^2=1$. The y - intercept is $y = 1$.

Step3: Analyze the sign of the function

Since $f(x)=(x + 1)^2(x - 1)^2$, and $(x + 1)^2\geq0$ and $(x - 1)^2\geq0$ for all real $x$, the function $f(x)\geq0$ for all $x\in R$.

Answer:

The x - intercepts are $x=-1$ and $x = 1$. The y - intercept is $y = 1$. The function is non - negative for all real $x$. Plot the points $(-1,0)$, $(1,0)$ and $(0,1)$ on the graph.