let the graph of g be a translation of 3 units right and 2 units up, followed by a reflection of the x-axis of f(x)=x^2-5x. Write a rule for g

Answer 1

There is also a reflection across the x-axis.

So the final function rule is h(x) = -(x-3)² + 5(x-3) - 2.

Reflection over the x-axis changes all the signs: + to -, and - to +.

Answer 2

Translation to the left or right means you will add or subtract something from the "x" because "x" is the variable associated with left/right. The only thing is that "x" is like Mr. Opposite. You must do the opposite of the way it reads. So when it says right by 3, you group a negative 3 with the "x".

So f(x) = x² - 5x becomes y = (x - 3)² - 5(x - 3)

Translation up or down means you will add or subtract from the "y" because "y" is the variable associated with up/down. To do so, just add or subtract a number at the end of the function. And you do so the way it reads so 2 units up means add 2.

So y = (x - 3)² - 5(x - 3)

A reflection over the x-axis means we add a negative sign out front so:

y = -[(x - 3)² - 5(x - 3) + 2]

or g(x) = -(x - 3)² + 5(x - 3) - 2

This can be multiplied out to put it in standard form if desired.