consider the following function.\nu(x)=\begin{cases}-2x - 6&\text{if }xleq - 3\\\frac{1}{3}x^{2}&\text{if }x…

consider the following function.\nu(x)=\begin{cases}-2x - 6&\text{if }xleq - 3\\\frac{1}{3}x^{2}&\text{if }x > - 3end{cases}\nstep 1 of 3: identify the general shape and direction of the graph of this function on the interval ((-infty,-3).

consider the following function.\nu(x)=\begin{cases}-2x - 6&\text{if }xleq - 3\\\frac{1}{3}x^{2}&\text{if }x > - 3end{cases}\nstep 1 of 3: identify the general shape and direction of the graph of this function on the interval ((-infty,-3).

Answer

Explanation:

Step1: Analyze the function for $x\leq - 3$

The function is $u(x)=-2x - 6$ for $x\leq - 3$. This is a linear - function in the form $y = mx + b$, where $m=-2$ and $b = - 6$.

Step2: Determine the shape and direction

Since the slope $m=-2<0$, the graph of the function $u(x)=-2x - 6$ on the interval $(-\infty,-3]$ is a straight - line that is decreasing.

Answer:

The graph is a straight - line and is decreasing.