Question

Which function, g(x), represents the function f(x)=(x+2)²-1 with a vertical shift 3 units down and a horizontal shift 5 units to the right?a) g(x)=(x-3)²+2b) g(x)=(x-3)²-4c) g(x)=(x+7)²-4d) g(x)=(x+7)²+2

Answer 1

We can see that the parent function is

$f(x)=(x+2)^2-1$

now, we must translate 3 units down and 5 units to the right, This can be represented mathematically by

$(x,y)\Rightarrow(x+5,y+3)$

Hence we have that

$g(x)=((x+5)+2)^2-1)+3$

finally, we have that

$g(x)=(x+7)^2+2$