Answer:
1. Translation 3 units to the right;
2. Reflection across the x-axis;
3. Translation 4 units up.
Step-by-step explanation:
First, rewrite the function [tex]g(x)[/tex] in following way:
[tex]g(x)=-x^2+6x-5=-(x^2-6x)-5=-(x^2-6x+9-9)-5=-(x-3)^2+9-5=-(x-3)^2+4.[/tex]
Apply such transformations:
1. Translate the graph of the parent function [tex]f(x)[/tex] 3 units to the right to get the graph of the function [tex]f_1(x)=(x-3)^2.[/tex]
2. Reflect the graph of the function [tex]f_1(x)[/tex] across the x-axis to get the graph of the function [tex]f_2(x)=-(x-3)^2.[/tex]
3. Translate the graph of the function [tex]f_2(x)[/tex] 4 units up to get the graph of the function [tex]g(x)=-(x-3)^2+4.[/tex]
