Answer:
[tex]g(x)=1.5^{x}-4[/tex]
Step-by-step explanation:
we have
[tex]f(x)=1.5^{x}[/tex]
the y-intercept of the function f(x) is for x equal zero
so
[tex]f(0)=1.5^{0}=1[/tex]
The y-intercept of f(x) is the point [tex](0,1)[/tex]
The function g(x) in the graph has the y-intercept equal to [tex]-3[/tex]
The y-intercept of g(x) is the point [tex](0,-3)[/tex]
therefore
the rule of the translation is
[tex](0,1)------->(0,-3) [/tex]
[tex](x,y)------->(x,y-4) [/tex]
that means
the translation is [tex]4[/tex] units down
the equation of g(x) is equal to
[tex]g(x)=1.5^{x}-4[/tex]
