Q:

Consider the graph given below.Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above.Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 unitsShift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 unitsShift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2

Accepted Solution

A:
check the picture below.

from the original blue line, it went to the green, then to the red one and then it ended on the purple one.

shifted by 3 units to the right.

reflected over the y-axis.

stretched vertically by a factor of 2.

or

you can also

reflect over the y-axis

stretch it by a factor of 2

and shift it upwards by 6 units, that'll have the same effect.

or rearrange the first set,

shift by 3 units first

reflect over the y-axis

and then stretch by a factor of 2.

is pretty much the same steps just rearranged.