Answer:
1). g(x) = [tex]5^{3x}[/tex]
2). g(x) = [tex]\frac{1}{3}5^{x}[/tex]
3). g(x) = [tex]3(5)^{x}[/tex]
4). g(x) = [tex]5^{\frac{1}{3}x}[/tex]
Step-by-step explanation:
Parent function f(x) = [tex]a^{x}[/tex] when transformed in the form of [tex]g(x)=h(a^{\frac{x}{k} })[/tex]
1). If h > 1, function is vertically stretched.
2). If 0 < h < 1, function is vertically compressed.
3). If k > 1, function is horizontally compressed.
4). If 0 < k < 1, function is horizontally stretched.
Parent function of the given functions in the question is f(x) = [tex]5^{x}[/tex]
g(x)= [tex]\frac{1}{3}(5^{x})[/tex], parent function is vertically compressed by a factor of [tex]\frac{1}{3}[/tex].
g(x) = [tex]5^{3x}[/tex], parent function 'f' is horizontally stretched by a factor of 3.
g(x) = [tex]5^{\frac{x}{3}}[/tex], parent function 'f' is horizontally compressed by a factor of [tex]\frac{1}{3}[/tex].
g(x) = [tex]3(5^{x})[/tex], parent function 'f' is vertically stretched by a factor of 3.
