Question

consider the following function. step 1 of 2: identify the general shape of the graph of this function. $g(x)=-\frac{5}{2}|x|$

Explanation:

Step1: Recall absolute - value function properties

The general form of an absolute - value function is $y = a|x|$, where $a$ is a non - zero real number. Here, $a=-\frac{5}{2}$.

Step2: Analyze the effect of the coefficient

When $a>0$, the graph of $y = a|x|$ is a "V" shape opening upwards. When $a < 0$, the graph of $y=a|x|$ is a "V" shape opening downwards. Since $a =-\frac{5}{2}<0$, the graph of $g(x)=-\frac{5}{2}|x|$ is a "V" shape opening downwards.

Answer:

A "V" shape opening downwards.