Let the graph of g
be a vertical stretch by a factor of 4, followed by a translation 3 units to the right of the graph of f(x)=3x−2−−−−√−2
. Write a rule for g
.
1 thought on “Let the graph of g<br />
be a vertical stretch by a factor of 4, followed by a translation 3 units to the right of the graph of f”
Answer:
We may rewrite f(x) = (x-1)^2
We stretch by having 3(x-1)^2
We reflect about the y axis by changing x to -x: 3(-x-1)^2 = 3(x+1)^2
We move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2
A way to verify this: Consider y = x^2 to be the unit parabola. f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1; moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2
Answer:
We may rewrite f(x) = (x-1)^2
We stretch by having 3(x-1)^2
We reflect about the y axis by changing x to -x: 3(-x-1)^2 = 3(x+1)^2
We move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2
A way to verify this: Consider y = x^2 to be the unit parabola. f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1; moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2
We may write g(x) = 3x^2 + 18x + 27, also.
Hope it helps you mate..