how does the graph of f(x)= 1/2(3)^x+2 -1 relate to its parent function?the answers are the parent function has been translated to the leftthe parent function has been translated downthe parent function has been compressed

Answer:1) Translated to left by 2 unit.2) Translated down by 1 unit.3) Compressed vertically by 1/2 unit.Step-by-step explanation:Given :  Graph of the function [tex]f(x)=\frac{1}{2}(3)^{x+2}-1[/tex]To find : How does f(x) relates to its parent function.Solution : First we figure out its parent function Parent function is the simplest form of the function.f(x) parent function is [tex]g(x)=3^x[/tex]Now, how f(x) relates to g(x)1. The parent function has been translated to the left.Translated to left meansf(x)→f(x+b) , graph of f(x) has been translated by b unit.In g(x)→g(x+2), graph of g(x) has been translated by 2 unit.→The graph of g(x) has been translated to the left by 2 unit in the graph of f(x).2)The parent function has been translated to the down.Translated to down meansf(x)→f(x)-b , graph of f(x) has been translated left by b unit.In g(x)→g(x)-1, graph of g(x) has been translated down by 1 unit.→The graph of g(x) has been translated to the down by 1 unit in the graph of f(x).3)The parent function has been compressed.Compressed meansf(x)→a g(x) , graph of f(x) has been compressed by a unit.In g(x)→(1/2)f(x), graph of g(x) has been compressed vertically by 1/2 unit.→The graph of g(x) has been compressed vertically by 1/2 unit in the graph of f(x).