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 means
f(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 means
f(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 means
f(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).
