Answer
(a) The point on the graph of y = ƒ(x + 3) – 5 is (-2,2).
(b) The point on the graph of y = - 2ƒ(x - 2) + 1 is (3,-5).
(c) The point on the graph of y = ƒ(2x + 3) is (-1,3).
Work Step by Step
To obtain the point, first we find the points on the graph of ƒ(x + 3).
Horizontally shift left 3 units; subtract 3 from the x-coordinate on the graph of y = ƒ(x).
We get (-2,3).
Next we find the points on the graph of y = ƒ(x + 3) – 5.
Vertically shift down 5 units; subtract 5 from the y-coordinate on the graph of ƒ(x + 3).
We get (-2,-2).
To obtain the point, first we find the points on the graph of y = ƒ(x - 2).
Horizontally shift right 2 units; add 2 to the x-coordinate on the graph of y = ƒ(x).
We get (3,3).
Next we find the points on the graph of y = -2ƒ(x – 2).
Vertically stretch by a factor of -2; multiply by -2 for the y-coordinate on the graph of
y = ƒ(x - 2).
We get (3,-6).
Next we find the points on the graph of y = -2ƒ(x - 2) + 1.
Vertically shift up 1 unit; add 1 to the y-coordinate on the graph of y = -2ƒ(x – 2).
We get (3,-5).
(c)To find the point is on the graph of y = ƒ(2x + 3) .
To obtain the point, first we find the points on the graph of y = ƒ(2x).
Horizontally compress by a factor of 2; multiply by 2 for the x-coordinate on the graph of y = ƒ(x).
We get ( 2,3).
Next we find the points on the graph of y = ƒ(2x + 3).
Horizontally shift left 3 units; subtract 3 from the x-coordinate on the graph of y = ƒ(2).
We get (-1,3).
