Below is the graph of a function y=g(x): Carefully sketch the graph y=g(×+2)-1

Answer 1

if y = g(x)

then y = g(x+3) -1 is the same graph, same shape, but shifted 3 units to the left and down 1 unit.

if (x,y) is a point on g(x) then (x-3, y-1) is the corresponding point on g(x+3)-1

for example, if (1,2) is a point on g(x), then (1-3, 2-1) = (-2,1) is the corresponding point on g(x+3)+1

another example, if y=x^2 is h(x), then y=h(x+3)^2 -1 is the same upward opening parabola, but shifted left 3 units and down 1 unit. The vertex was (0,0) but now after the shifts left and down, the new vertex is (-3,-1)