Write a rule for g.

Question

Let the graph of g be a vertical stretch by a factor of 3 and reflect in the y-axis, followed by a translation 2 units left of the graph of f(x) = x^2-3x+1. Write a rule for g.

Answer 1

Hi Jordan:

Steching f(x) by 3 means finding 3*f(x)

reflecting about y-axis means f(-x)

translating by 2 units to the left means f(x+2)

So in steps. 3*f(x)= 3x²-9x+3

3*f(-x) = 3(-x)²-9*(-x) + 3 = 3x² + 9x + 3

translating by 2 units means 3*f(-(x+2)) = 3*(x+2)²+9*(x+2)+3