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$$\begin{array}{rl}\text{Question 1:}& \\ \text{a)}& g(x)=3^x+3\text{(Vertical shift up by 3 units)}\\ \text{b)}& g(x)=3^{x+3}\text{(Horizontal shift left by 3 units)}\\ \text{c)}& g(x)=\frac{1}{3}(3^x)\text{(Vertical compression by a factor of }\frac{1}{3})\\ \text{d)}& g(x)=3^{x/3}\text{(Horizontal stretch by a factor of 3)}.\\ \text{Question 2:}& \\ \text{a)}& f(x)=-3(4^{x+1})\\ & \text{Base function: }{4}^x\\ & \text{Transformations: Horizontal shift left by 1, Vertical stretch by 3, Reflection in }x\text{-axis.}\\ \text{b)}& g(x)=2{\left(\frac{1}{2}\right)}^{2x}+3\\ & \text{Base function: }{\left(\frac{1}{2}\right)}^x\\ & \text{Transformations: Horizontal compression by }\frac{1}{2},\text{ Vertical stretch by 2, Vertical shift up by 3.}\\ \text{c)}& h(x)=7(0.5^{x-4})-1\\ & \text{Base function: }0.5^x\\ & \text{Transformations: Horizontal shift right by 4, Vertical stretch by 7, Vertical shift down by 1.}\\ \text{d)}& k(x)=5^{3x-6}\\ & \text{Base function: }{5}^x\\ & \text{Transformations: Horizontal compression by }\frac{1}{3},\text{ Horizontal shift right by 2.}\end{array}$$ $$\begin{array}{rl}\text{Question 3:}& \\ \text{For each function in Questions 1 and 2:}& \\ \text{a) }g(x)=3^x+3:& \text{y-intercept: }4\\ & \text{Asymptote: }y=0\\ & \text{Domain: }(-\infty ,\infty )\\ & \text{Range: }(3,\infty )\\ \text{b) }g(x)=3^{x+3}:& \text{y-intercept: }27\\ & \text{Asymptote: }y=0\\ & \text{Domain: }(-\infty ,\infty )\\ & \text{Range: }(0,\infty )\\ \text{c) }g(x)=\frac{1}{3}(3^x):& \text{y-intercept: }\frac{1}{3}\\ & \text{Asymptote: }y=0\\ & \text{Domain: }(-\infty ,\infty )\\ & \text{Range: }(0,\infty )\\ \text{d) }g(x)=3^{x/3}:& \text{y-intercept: }1\\ & \text{Asymptote: }y=0\\ & \text{Domain: }(-\infty ,\infty )\\ & \text{Range: }(0,\infty )\\ \text{Question 4:}& \\ \text{a)}& g(x)=-{\left(\frac{1}{2}\right)}^{2x}\\ & \text{Base function: }{\left(\frac{1}{2}\right)}^x\\ & \text{Transformations: Horizontal compression by }\frac{1}{2},\text{ Reflection in }x\text{-axis.}\\ \text{b)}& g(x)=5{\left(\frac{1}{2}\right)}^{-(x-3)}\\ & \text{Base function: }{\left(\frac{1}{2}\right)}^x\\ & \text{Transformations: Horizontal reflection, Horizontal shift right by 3, Vertical stretch by 5.}\\ \text{c)}& g(x)=-4{\left(\frac{1}{2}\right)}^{3x+9}-6\\ & \text{Base function: }{\left(\frac{1}{2}\right)}^x\\ & \text{Transformations: Horizontal compression by }\frac{1}{3},\text{ Vertical stretch by 4, Reflection in }x\text{-axis, Vertical shift down by 6.}\end{array}$$