Find g(x), where g(x) is the translation 4 units right and 9 units down of f(x)= – 4x–6

Answer 1

f(x) = -4x-6

g(x) = -4(x-4) -6 -9

= -4x +16 -15

g(x) = -4x +1

take a more simple example y=x

shift it right 4 to get

y=x-4

graph it to see it better

shift down 9

y+9 = x-4

y=x-4-9

y =x-13

shifts down 9 means add 9, to y

shift right 4 means subtract 4, from x

Answer 2

Moving to the left or right is accomplished by adding (left) or subtracting (right) a number inside a set of parentheses around the varialbe. Moving up or down is accomplished by adding (up) or subtracting (down) a number outside a set of parentheses enclosing the variable. So, to perform the requested translation,

g(x)=-4(x-4)-6-9=-4(x-4)-15=-4x+16-15=-4x+1

because a 4 was subtracted (right) inside the parentheses and a 9 was subtracted (down) outside the parentheses.