graph the equation shown below by transforming the given graph of the parent function.\n\n$y=-2^{x}-3$\n\nsta…

Explanation:

Step1: Identify parent - function

The parent function of $y=-2^{x}-3$ is $y = 2^{x}$.

Step2: Reflect about x - axis

The negative sign in front of $2^{x}$ reflects the graph of $y = 2^{x}$ about the x - axis. So, if a point $(x,y)$ is on $y = 2^{x}$, the corresponding point on $y=-2^{x}$ is $(x, - y)$.

Step3: Translate down

The $- 3$ in $y=-2^{x}-3$ translates the graph of $y=-2^{x}$ down 3 units. If a point $(x,y)$ is on $y=-2^{x}$, the corresponding point on $y=-2^{x}-3$ is $(x,y - 3)$.

To graph:

1. For the parent function $y = 2^{x}$, some key points are $(0,1),(1,2),(2,4)$.
2. After reflection about the x - axis for $y=-2^{x}$, the points become $(0, - 1),(1,-2),(2,-4)$.
3. After translation down 3 units for $y=-2^{x}-3$, the points become $(0,-4),(1, - 5),(2,-7)$. Plot these points and draw a smooth curve.

Answer:

Graph the function $y=-2^{x}-3$ by first reflecting the graph of $y = 2^{x}$ about the x - axis and then translating it down 3 units. Plot key - points $(0,-4),(1, - 5),(2,-7)$ and draw a smooth curve.