transformations

Question

the graph of f(x)= squared x is translated 3 units down and reflected over the y-axis. What is the equation that represents the given transformation?

Answer 1

There are clever maths ways of combining transformations to find the resulting transformation. However, unfortunately, I'm not that clever. :-)

But, fortunately, this question doesn't need you to do any complicated transformations.

For f(x) = x² can you picture the curve?

It's a famous one, the parabola. The general equation is y = ax² + bx + c.

In this case a = 1, b=0, c=0, simplifying to y = x²

It passes through the origin (0,0) and it's symmetrical about the y axis (because square of negative number is positive).

Hence a reflection in the y axis (its axis of symmetry) would leave it unchanged. e.g. (1,1) -> (-1,1) but also (-1,1) -> (1,1) and (3,9) - > (-3,9) but also (-3,9) -> (3,9)

Fortunately, this property is preserved because the translation is down rather than across (i.e. doesn't change the axis of symmetry).

If y = x² passes through (0,0) [because 0²=0] and we translate down 3 units we get (0,-3)

This means the equation of the transformed function is y = x² - 3