Suppose (8,-2) is a point on the graph of y=g(x).

Question

Suppose (8,-2) is a point on the graph of y=g(x).

(a)What point is on the graph of y=g(x+4)-6

(b)What point is on the graph of y=-4g(x-8)+3

(c)What point is on the graph of y=g(4x+12)

Answer 1

8= g(2) for y=g(x), the point (2,8)

y=g(x+4)-6 shifts g(x) down 6 and left 4

y=8-6 = 2, x =2-4=-2, the point (-2,2)

y=-4g(x-8)+3 shifts g(x) up 3, right 8 and stretches vertically by a factor of 4, reflected across the x axis due to -4

x=2+8=10, y=4(8) =32, -32+3=-29

the point (10, -29)