Question

If the equation of the line is f(x) = 1/3x - 5 , what would be the new equation if there was a reflection over the y- axis, a dilation of -6, and a translation of 4 units up?

pls help I already solved but I'm not sure if I did a step out of order

Answer 1

Answer: Thus, after the transformation, the graph consists of points (x,y) satisfying y=2(x−3)2. This is the equation of the transformed graph.

Explanation:

Consider the graph y=x2. Suppose the graph is dilated from the x-axis by a factor of 2, and then translated 3 units to the right. What is the equation of the resulting graph?

Solution

The transformation given is Trans(3,0)∘Dilx-axis,2. Denote by (x′,y′) the image of a point (x,y) under this transformation. A point (x,y) is sent to (x,2y) by the dilation, and then to (x+3,2y) by the translation, so (x′,y′)=(x+3,2y).

The original graph consists of points (x,y) such that y=x2. Then it is transformed so that (x,y)↦(x′,y′)=(x+3,2y). We must find what equation is satisfied by x′ and y′.

Since x′=x+3 and y′=2y, we have x=x′−3 and y=y′/2. Thus y=x2 implies

y′2=(x′−3)2or equivalentlyy′=2(x′−3)2.