Respuesta :
Answer:
[tex]h(x)=4(3)^x[/tex]; Vertical stretch
[tex]g(x)=(3)^{5x}[/tex]; Horizontal compression
[tex]p(x)=\frac{1}{2}(3)^x[/tex]; Vertical compression
[tex]w(x)=(3)^{0.2x}[/tex]; Horizontal stretch
Step-by-step explanation:
The given parent function is
[tex]f(x)=3^x[/tex]
The transformation between two functions is defined as
[tex]q(x)=kf(x)[/tex]
If 0<k<1, then it is vertical compression and k>1 then it is vertical stretch.
[tex]q(x)=f(jx)[/tex]
If 0<j<1, then it is horizontal stretch and j>1 then it is horizontal compression.
[tex]h(x)=4(3)^x[/tex]
[tex]h(x)=4f(x)[/tex]
Here, k=4, therefore it is vertical stretch.
[tex]g(x)=(3)^{5x}[/tex]
[tex]g(x)=f(5x)[/tex]
Here, j=5, therefore it is horizontal compression.
[tex]p(x)=\frac{1}{2}(3)^x[/tex]
[tex]p(x)=\frac{1}{2}f(x)[/tex]
Here, k=1/2, therefore it is vertical compression.
[tex]w(x)=(3)^{0.2x}[/tex]
[tex]w(x)=f(0.2x)[/tex]
Here, j=0.2, therefore it is horizontal stretch.
