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

Answer:

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

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 ): [ \begin{align*} f(-3)&=-3(2)^{-3 + 3}-3\ &=-3(2)^{0}-3\ &=-3\times1 - 3\ &=-6 \end{align*} ] Let ( x=-2 ): [ \begin{align*} f(-2)&=-3(2)^{-2 + 3}-3\ &=-3(2)^{1}-3\ &=-3\times2-3\ &=-9 \end{align*} ]