draw the graph of f(x)= - 3^x\nquestion help: video message instructor\nnext question

Explanation:

Step1: Find key - points

Choose some values of (x). When (x = 0), (f(0)=-3^{0}=- 1); when (x = 1), (f(1)=-3^{1}=-3); when (x = 2), (f(2)=-3^{2}=-9); as (x\to-\infty), (3^{x}\to0), so (f(x)\to0) (but (f(x)<0)).

Step2: Analyze the behavior

The function (y = 3^{x}) is an exponential growth function. The function (y=-3^{x}) is a reflection of (y = 3^{x}) about the (x) - axis. It is always negative, and it is a decreasing function since the base (a = 3>1) and the negative sign in front flips its behavior.

Step3: Plot the points and draw the curve

Plot the points ((0, - 1)), ((1,-3)), ((2, - 9)) and use the fact that as (x\to-\infty), (y\to0) (from below) to draw a smooth - decreasing curve that approaches the (x) - axis (but never touches it since (y<0)) for negative (x) values.

Answer:

Plot the points ((0,-1)), ((1, - 3)), ((2,-9)) and draw a decreasing curve that approaches the (x) - axis from below as (x\to-\infty).