#$&*
course Mth 163
Make tables and sketch graphs of y = x, y = x 2 , y = x -1 and y = 2 x , for x = -3 to x = 3. •Show what happens to each graph if it is vertically stretched by factor 2.
Y=x transformed to y=2x changes the slope of the line from 1/1 to 2/2, causing the incline to increase.
X Y1 Y2
-3 -3 -6
-2 -2 -4
-1 -1 -2
0 0 0
1 1 2
2 2 4
3 3 6
Y=x^2 tranformed to y=2x^2 stretches the graph by multiples of 2 on the y axis.
X Y1 Y2
-3 9 18
-2 4 8
-1 1 2
0 0 0
1 1 2
2 4 8
3 9 18
Y=x^-1 transformed to y=2x^-1 stretches the graph by one unit, the stretch decreasing by fractional margins each time.
X Y1 Y2
-3 -0.3333333 -0.6666666667
-2 -0.5 -1
-1 -1 -2
0 Asymptote Asymptote
1 1 2
2 0.5 1
3 0.3333333 0.666666666667
Y=2^x transformed to y=4^x stretches the graph by the multiple of 2, causing the graph to become more steep.
X Y1 Y2
-3 0.125 0.01563
-2 0.25 0.0625
-1 0.5 0.25
0 1 1
1 2 4
2 4 16
3 8 64
&#This looks good. Let me know if you have any questions. &#