Question

Algebra 2 Help? (Connections Academy)
1.) the graph of g(x) is f(x) translated to the left 7 units and down 3 units. What is the function rule for g(x) given f(x) = x^2?
2.) for g(x)= |3x+2| + 6, find g(-4).

Answer 1

1.) g(x) = f(x+7)-3

Formula for horizontal translations: g(x)=f(x-h)
h being the distance translated, If the translation is right-substitute h with the positive number; if the translation is left-substitute h with the negative number.

Formula for vertical translations: g(x)= f(x)-k
k being the distance translated, If the translation is up- substitute k with the positive number; if the translation is down-substitute k with the negative number... Hope this helps!

2.) g(-4)=|3x+2|+6
g(-4)=|3(-4)+2|+6
g(-4)=|-12+2|+6
g(-4)=|-10|+6
g(-4)=10+6
g(-4)=16

Just remember for g(x) the x in parenthesis is the x in the equation, so you can just substitute and then solve.