Question

graph the function ( f(x)=-3(2)^{x + 3}-3 ) on the axes below. you must plot the asymptote and any two points with integer coordinates.
asymptote:

Explanation:

Step1: Find the asymptote

For an exponential function of the form \( y = a(b)^{x - h}+k \), the horizontal asymptote is \( y = k \).
In the function \( f(x)=-3(2)^{x + 3}-3 \), comparing with \( y = a(b)^{x - h}+k \), we have \( k=-3 \). So the horizontal asymptote is \( y=-3 \).

Step2: Find points with integer coordinates

Let \( x=-3 \):

$$
LATEXBLOCK0
$$

Let \( x=-2 \):

$$
LATEXBLOCK1
$$

Answer:

Asymptote: \( y = - 3 \)
Points: \((-3,-6)\) and \((-2,-9)\)